Sur la distribution des zéros de la fonction et ses conséquences arithmétiques
Bulletin de la Société Mathématique de France, Tome 24 (1896), pp. 199-220.
@article{BSMF_1896__24__199_1, author = {Hadamard, J.}, title = {Sur la distribution des z\'eros de la fonction $\zeta (s)$ et ses cons\'equences arithm\'etiques}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {199--220}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {24}, year = {1896}, doi = {10.24033/bsmf.545}, language = {fr}, url = {https://www.numdam.org/articles/10.24033/bsmf.545/} }
TY - JOUR AU - Hadamard, J. TI - Sur la distribution des zéros de la fonction $\zeta (s)$ et ses conséquences arithmétiques JO - Bulletin de la Société Mathématique de France PY - 1896 SP - 199 EP - 220 VL - 24 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.545/ DO - 10.24033/bsmf.545 LA - fr ID - BSMF_1896__24__199_1 ER -
%0 Journal Article %A Hadamard, J. %T Sur la distribution des zéros de la fonction $\zeta (s)$ et ses conséquences arithmétiques %J Bulletin de la Société Mathématique de France %D 1896 %P 199-220 %V 24 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.545/ %R 10.24033/bsmf.545 %G fr %F BSMF_1896__24__199_1
Hadamard, J. Sur la distribution des zéros de la fonction $\zeta (s)$ et ses conséquences arithmétiques. Bulletin de la Société Mathématique de France, Tome 24 (1896), pp. 199-220. doi : 10.24033/bsmf.545. https://www.numdam.org/articles/10.24033/bsmf.545/
- Some Properties and Algorithms for Twin Primes, Applied Sciences, Volume 14 (2024) no. 17, p. 7902 | DOI:10.3390/app14177902
- « Sans amour et sans haine » : la Grande Guerre de Jacques Hadamard, Cahiers François Viète, Volume III-16 (2024), p. 169 | DOI:10.4000/11qww
- USING IFS TO REVEAL BIASES IN THE DISTRIBUTION OF PRIME NUMBERS, Fractals, Volume 32 (2024) no. 06 | DOI:10.1142/s0218348x24501032
- The Values of Mathematical Proofs, Handbook of the History and Philosophy of Mathematical Practice (2024), p. 2081 | DOI:10.1007/978-3-031-40846-5_34
- Dense clusters of zeros near the zero-free region of ζ(s), International Journal of Number Theory, Volume 20 (2024) no. 04, p. 1017 | DOI:10.1142/s1793042124500520
- Heuristically Sifting Twins, Resonance, Volume 28 (2024) no. 10, p. 1505 | DOI:10.1007/s12045-023-1687-0
- On the binary Goldbach conjecture under primorial-based constraints, SSRN Electronic Journal (2024) | DOI:10.2139/ssrn.4839110
- Geometric Features of the Hurwitz–Lerch Zeta Type Function Based on Differential Subordination Method, Symmetry, Volume 16 (2024) no. 7, p. 784 | DOI:10.3390/sym16070784
- On the Primorial Counting Function, The American Mathematical Monthly, Volume 131 (2024) no. 5, p. 433 | DOI:10.1080/00029890.2024.2309123
- , 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) (2023), p. 1426 | DOI:10.1109/focs57990.2023.00088
- New estimates for some integrals of functions defined over primes, Functiones et Approximatio Commentarii Mathematici, Volume 68 (2023) no. 2 | DOI:10.7169/facm/2049
- Holographic realization of the prime number quantum potential, PNAS Nexus, Volume 2 (2023) no. 1 | DOI:10.1093/pnasnexus/pgac279
- Adaptive low-depth quantum algorithms for robust multiple-phase estimation, Physical Review A, Volume 108 (2023) no. 6 | DOI:10.1103/physreva.108.062408
- Zeros of derivatives of 𝐿-functions in the Selberg class on ℜ(𝑠)<1/2, Proceedings of the American Mathematical Society (2023) | DOI:10.1090/proc/16251
- The Green-Tao Theorem and the Infinitude of Primes in Domains, The American Mathematical Monthly, Volume 130 (2023) no. 2, p. 114 | DOI:10.1080/00029890.2022.2141543
- SZEMERÉDI’S THEOREM: AN EXPLORATION OF IMPURITY, EXPLANATION, AND CONTENT, The Review of Symbolic Logic, Volume 16 (2023) no. 3, p. 700 | DOI:10.1017/s1755020321000538
- An Operator Theoretic Approach to the Prime Number Theorem, Zurnal matematiceskoj fiziki, analiza, geometrii, Volume 19 (2023) no. 1, p. 172 | DOI:10.15407/mag19.01.172
- On Some Algebraic Ways to Calculate Zeros of the Riemann Zeta Function, Algebraic Informatics, Volume 13706 (2022), p. 15 | DOI:10.1007/978-3-031-19685-0_2
- Advances in additive number theory, Boletim da Sociedade Paranaense de Matemática, Volume 41 (2022), p. 1 | DOI:10.5269/bspm.51233
- Proving the Prime Number Theorem, Excursions in Multiplicative Number Theory (2022), p. 233 | DOI:10.1007/978-3-030-73169-4_23
- Asymptotic expansions of the prime counting function, Journal of Number Theory, Volume 238 (2022), p. 353 | DOI:10.1016/j.jnt.2021.07.032
- Unconditional explicit Mertens’ theorems for number fields and Dedekind zeta residue bounds, The Ramanujan Journal, Volume 57 (2022) no. 3, p. 1169 | DOI:10.1007/s11139-021-00435-6
- Die natürlichen Zahlen, Von den natürlichen Zahlen zu den Quaternionen (2022), p. 9 | DOI:10.1007/978-3-658-36621-6_1
- Rényi 100, Quantitative and qualitative (in)dependence, Acta Mathematica Hungarica, Volume 165 (2021) no. 1, p. 218 | DOI:10.1007/s10474-021-01164-4
- Multidimensional scaling and visualization of patterns in distribution of nontrivial zeros of the zeta-function, Communications in Nonlinear Science and Numerical Simulation, Volume 102 (2021), p. 105924 | DOI:10.1016/j.cnsns.2021.105924
- The Values of Mathematical Proofs, Handbook of the History and Philosophy of Mathematical Practice (2021), p. 1 | DOI:10.1007/978-3-030-19071-2_34-1
- Proof the Skewes’ number is not an integer using lattice points and tangent line, Journal of Applied Mathematics, Statistics and Informatics, Volume 17 (2021) no. 2, p. 5 | DOI:10.2478/jamsi-2021-0006
- Speeding-up verification of digital signatures, Journal of Computer and System Sciences, Volume 116 (2021), p. 22 | DOI:10.1016/j.jcss.2020.08.005
- Prime zeta function statistics and Riemann zero-difference repulsion, Journal of Statistical Mechanics: Theory and Experiment, Volume 2021 (2021) no. 7, p. 073206 | DOI:10.1088/1742-5468/ac0ee0
- Sharper bounds for the Chebyshev function 𝜃(𝑥), Mathematics of Computation, Volume 90 (2021) no. 331, p. 2281 | DOI:10.1090/mcom/3643
- The Approximability of Multiple Facility Location on Directed Networks with Random Arc Failures, Algorithmica, Volume 82 (2020) no. 9, p. 2474 | DOI:10.1007/s00453-020-00693-8
- Multidimensional scaling and visualization of patterns in prime numbers, Communications in Nonlinear Science and Numerical Simulation, Volume 83 (2020), p. 105128 | DOI:10.1016/j.cnsns.2019.105128
- New Proof That the Sum of the Reciprocals of Primes Diverges, Mathematics, Volume 8 (2020) no. 9, p. 1414 | DOI:10.3390/math8091414
- Subdiffusive light transport in three-dimensional subrandom arrays, Physical Review B, Volume 101 (2020) no. 21 | DOI:10.1103/physrevb.101.214204
- Gauss on Gaussian Quadrature, The American Mathematical Monthly, Volume 127 (2020) no. 2, p. 125 | DOI:10.1080/00029890.2020.1680201
- The Riemann Hypothesis in computer science, Theoretical Computer Science, Volume 807 (2020), p. 257 | DOI:10.1016/j.tcs.2019.07.028
- Counting Closed Orbits in Discrete Dynamical Systems, Dynamical Systems, Bifurcation Analysis and Applications, Volume 295 (2019), p. 147 | DOI:10.1007/978-981-32-9832-3_9
- Constraint-Based Privacy Preserving-Path Computation Element, International Journal of Smart Security Technologies, Volume 6 (2019) no. 2, p. 1 | DOI:10.4018/ijsst.2019070101
- Hidden multiscale order in the primes, Journal of Physics A: Mathematical and Theoretical, Volume 52 (2019) no. 13, p. 135002 | DOI:10.1088/1751-8121/ab0588
- Power-free Values of Strongly
-additive Functions, Taiwanese Journal of Mathematics, Volume 23 (2019) no. 4 | DOI:10.11650/tjm/181208 - On Prime Spectrum of Maximal Subgroups in Finite Groups, Algebra Colloquium, Volume 25 (2018) no. 04, p. 579 | DOI:10.1142/s1005386718000408
- Explicit bounds for primes in arithmetic progressions, Illinois Journal of Mathematics, Volume 62 (2018) no. 1-4 | DOI:10.1215/ijm/1552442669
- On Sarnak’s conjecture and Veech’s question for interval exchanges, Journal d'Analyse Mathématique, Volume 134 (2018) no. 2, p. 545 | DOI:10.1007/s11854-018-0017-z
- The structure factor of primes, Journal of Physics A: Mathematical and Theoretical, Volume 51 (2018) no. 11, p. 115001 | DOI:10.1088/1751-8121/aaa52a
- Uncovering multiscale order in the prime numbers via scattering, Journal of Statistical Mechanics: Theory and Experiment, Volume 2018 (2018) no. 9, p. 093401 | DOI:10.1088/1742-5468/aad6be
- Morphogenesis of the Zeta Function in the Critical Strip by Computational Approach, Mathematics, Volume 6 (2018) no. 12, p. 285 | DOI:10.3390/math6120285
- Equivalent formulations of the Riemann hypothesis based on lines of constant phase, Physica Scripta, Volume 93 (2018) no. 6, p. 065201 | DOI:10.1088/1402-4896/aabca9
- , Volume 1905 (2017), p. 030024 | DOI:10.1063/1.5012170
- , 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS) (2017), p. 651 | DOI:10.1109/mwscas.2017.8053007
- Recent results about the prime ideal theorem, Bollettino dell'Unione Matematica Italiana, Volume 10 (2017) no. 1, p. 19 | DOI:10.1007/s40574-016-0084-y
- The Natural Numbers, From Natural Numbers to Quaternions (2017), p. 9 | DOI:10.1007/978-3-319-69429-0_1
- Riemann Surfaces: Reception by the French School, From Riemann to Differential Geometry and Relativity (2017), p. 237 | DOI:10.1007/978-3-319-60039-0_8
- Remarks on Simple Proofs, Simplicity: Ideals of Practice in Mathematics and the Arts (2017), p. 143 | DOI:10.1007/978-3-319-53385-8_12
- On the Alleged Simplicity of Impure Proof, Simplicity: Ideals of Practice in Mathematics and the Arts (2017), p. 205 | DOI:10.1007/978-3-319-53385-8_16
- E29: One Old Erdős–Turán Problem, The Colorado Mathematical Olympiad: The Third Decade and Further Explorations (2017), p. 217 | DOI:10.1007/978-3-319-52861-8_21
- Digital functions and sums involving the largest prime factor of an integer, Acta Mathematica Hungarica, Volume 149 (2016) no. 2, p. 396 | DOI:10.1007/s10474-016-0580-7
- STRONGLY -ADDITIVE FUNCTIONS AND DISTRIBUTIONAL PROPERTIES OF THE LARGEST PRIME FACTOR, Bulletin of the Australian Mathematical Society, Volume 93 (2016) no. 2, p. 177 | DOI:10.1017/s0004972715001264
- Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz, From Arithmetic to Zeta-Functions (2016), p. 309 | DOI:10.1007/978-3-319-28203-9_20
- From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, Open Problems in Mathematics (2016), p. 123 | DOI:10.1007/978-3-319-32162-2_2
- Beatty sequences and prime numbers with restrictions on strongly q-additive functions, Periodica Mathematica Hungarica, Volume 72 (2016) no. 2, p. 139 | DOI:10.1007/s10998-016-0114-7
- A correspondence principle, Physica A: Statistical Mechanics and its Applications, Volume 443 (2016), p. 495 | DOI:10.1016/j.physa.2015.09.024
- CHARACTER AND OBJECT, The Review of Symbolic Logic, Volume 9 (2016) no. 3, p. 480 | DOI:10.1017/s1755020315000398
- A Scale Invariant Distribution of the Prime Numbers, Computation, Volume 3 (2015) no. 4, p. 528 | DOI:10.3390/computation3040528
- Some special primes and square sums, Quaestiones Mathematicae, Volume 38 (2015) no. 1, p. 57 | DOI:10.2989/16073606.2014.981705
- The Prime Number Theorem, Why Prove it Again? (2015), p. 111 | DOI:10.1007/978-3-319-17368-9_10
- Levels of Distribution and the Affine Sieve, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 23 (2014) no. 5, p. 933 | DOI:10.5802/afst.1432
- The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression, Archive for History of Exact Sciences, Volume 68 (2014) no. 3, p. 265 | DOI:10.1007/s00407-013-0126-0
- Sur les chiffres des nombres premiers translatés, Functiones et Approximatio Commentarii Mathematici, Volume 51 (2014) no. 2 | DOI:10.7169/facm/2014.51.2.2
- New extensions of some classical theorems in number theory, Journal of Number Theory, Volume 133 (2013) no. 11, p. 3771 | DOI:10.1016/j.jnt.2013.05.011
- The Heritage, Rational Number Theory in the 20th Century (2012), p. 1 | DOI:10.1007/978-0-85729-532-3_1
- The First Years, Rational Number Theory in the 20th Century (2012), p. 13 | DOI:10.1007/978-0-85729-532-3_2
- Thermodynamic functions of ZrW2O8 from its heat capacity, Science China Physics, Mechanics and Astronomy, Volume 55 (2012) no. 4, p. 563 | DOI:10.1007/s11433-012-4667-z
- Arithmetical approach to the twin primes conjecture, ANNALI DELL'UNIVERSITA' DI FERRARA, Volume 57 (2011) no. 1, p. 191 | DOI:10.1007/s11565-009-0070-8
- Testing Periodicity, Algorithmica, Volume 60 (2011) no. 2, p. 401 | DOI:10.1007/s00453-009-9351-y
- Structure and Randomness in the Prime Numbers, An Invitation to Mathematics (2011), p. 1 | DOI:10.1007/978-3-642-19533-4_1
- The impact of 𝜁(𝑠) complex zeros on 𝜋(𝑥) for 𝑥<10^10¹³, Mathematics of Computation, Volume 80 (2011) no. 276, p. 2381 | DOI:10.1090/s0025-5718-2011-02477-4
- Colloquium: Physics of the Riemann hypothesis, Reviews of Modern Physics, Volume 83 (2011) no. 2, p. 307 | DOI:10.1103/revmodphys.83.307
- Some Direct and Remote Relations of Gauss with Belgian Mathematicians, Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 112 (2010) no. 2, p. 99 | DOI:10.1365/s13291-010-0002-7
- Combinatorics, Mathematics and Its History (2010), p. 553 | DOI:10.1007/978-1-4419-6053-5_25
- Proof Theory in Philosophy of Mathematics, Philosophy Compass, Volume 5 (2010) no. 4, p. 336 | DOI:10.1111/j.1747-9991.2010.00282.x
- Zionist Internationalism through Number Theory: Edmund Landau at the Opening of the Hebrew University in 1925, Science in Context, Volume 23 (2010) no. 4, p. 427 | DOI:10.1017/s0269889710000177
- Formeln und Zahlen, Bilder der Mathematik (2009), p. 46 | DOI:10.1007/978-3-8274-2181-4_4
- Die Riemannsche Vermutung, Mathematisch für Anfänger (2009), p. 277 | DOI:10.1007/978-3-8274-2286-6_21
- Nuclei, Primes and the Random Matrix Connection, Symmetry, Volume 1 (2009) no. 1, p. 64 | DOI:10.3390/sym1010064
- Quantum mechanical potentials related to the prime numbers and Riemann zeros, Physical Review E, Volume 78 (2008) no. 5 | DOI:10.1103/physreve.78.056215
- Testing Periodicity, Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques, Volume 3624 (2005), p. 366 | DOI:10.1007/11538462_31
- The Average Amount of Information Lost in Multiplication, IEEE Transactions on Information Theory, Volume 51 (2005) no. 2, p. 684 | DOI:10.1109/tit.2004.840866
- Literature, The History of Mathematics (2005), p. 561 | DOI:10.1002/9781118033098.refs
- A unified solution of the specific-heat–phonon spectrum inversion problem, Europhysics Letters (EPL), Volume 61 (2003) no. 6, p. 723 | DOI:10.1209/epl/i2003-00288-6
- Phonon spectrum of YBCO obtained by specific heat inversion method for real data, Journal of Physics: Condensed Matter, Volume 15 (2003) no. 2, p. 225 | DOI:10.1088/0953-8984/15/2/322
- Properties of Prime Numbers, Topics in the Theory of Numbers (2003), p. 157 | DOI:10.1007/978-1-4613-0015-1_5
- A century of complex Tauberian theory, Bulletin of the American Mathematical Society, Volume 39 (2002) no. 4, p. 475 | DOI:10.1090/s0273-0979-02-00951-5
- Some Aspects of Interactions between Algebraic Number Theory and Analytic Number Theory, Number Theoretic Methods, Volume 8 (2002), p. 263 | DOI:10.1007/978-1-4757-3675-5_14
- On the Number of Cycles of p-adic Dynamical Systems, Journal of Number Theory, Volume 90 (2001) no. 2, p. 255 | DOI:10.1006/jnth.2001.2665
- Adventures In Arithmetick, or: How to Make Good Use of a Fourier Transform, Mathematical Conversations (2001), p. 87 | DOI:10.1007/978-1-4613-0195-0_9
- Type of inversion problem in physics: An inverse emissivity problem, Physical Review E, Volume 63 (2001) no. 4 | DOI:10.1103/physreve.63.045601
- A Centennial History of the Prime Number Theorem, Number Theory (2000), p. 1 | DOI:10.1007/978-3-0348-7023-8_1
- A Centennial History of the Prime Number Theorem, Number Theory (2000), p. 1 | DOI:10.1007/978-93-86279-02-6_1
- An Explicit Zero-Free Region for the Riemann Zeta-Function, Rocky Mountain Journal of Mathematics, Volume 30 (2000) no. 1 | DOI:10.1216/rmjm/1022008980
- A concrete realization of specific heat-phonon spectrum inversion for YBCO, Physics Letters A, Volume 264 (1999) no. 1, p. 68 | DOI:10.1016/s0375-9601(99)00761-6
- Umweltforschung zwischen Formalwissenschaft und Verständnis: Muß man den Formalismus beherrschen, um die Formalisten zu schlagen?, Umweltforschung quergedacht (1998), p. 309 | DOI:10.1007/978-3-642-58801-3_14
- A direct approach to the mellin transform, The Journal of Fourier Analysis and Applications, Volume 3 (1997) no. 4, p. 325 | DOI:10.1007/bf02649101
- Empirical Methods in Mathematics, Spanish Studies in the Philosophy of Science, Volume 186 (1996), p. 19 | DOI:10.1007/978-94-009-0305-0_2
- A Hundred Years of Prime Numbers, The American Mathematical Monthly, Volume 103 (1996) no. 9, p. 729 | DOI:10.1080/00029890.1996.12004813
- Асимптотическое распределение простых чисел в среднем, Успехи математических наук, Volume 51 (1996) no. 6, p. 21 | DOI:10.4213/rm1018
- Is there any Regularity in the Distribution of Prime Numbers at the Beginning of the Sequence of Positive Integers?, Mathematics Magazine, Volume 68 (1995) no. 2, p. 110 | DOI:10.1080/0025570x.1995.11996292
- Die neuere Entwicklung der analytischen Zahlentheorie, Harald Cramér Collected Works (1994), p. 289 | DOI:10.1007/978-3-642-61221-3_19
- The local behaviour of some additive functions, Acta Mathematica Hungarica, Volume 62 (1993) no. 3-4, p. 363 | DOI:10.1007/bf01874656
- Die Nullstellen der Riemannschen Zetafunktion, Mathematische Semesterberichte, Volume 39 (1992) no. 2, p. 185 | DOI:10.1007/bf03186469
- Staircase functions, spectral rigidity, and a rule for quantizing chaos, Physical Review A, Volume 45 (1992) no. 2, p. 583 | DOI:10.1103/physreva.45.583
- Bibliography, The Riemann Zeta-Function (1992), p. 385 | DOI:10.1515/9783110886146.385
- On the relation between the phonon spectrum and the specific heat, Physics Letters A, Volume 152 (1991) no. 7, p. 323 | DOI:10.1016/0375-9601(91)90731-m
- H, Encyclopaedia of Mathematics (1989), p. 344 | DOI:10.1007/978-94-009-5997-2_3
- Applications of the Normal Form in Mechanics, Local Methods in Nonlinear Differential Equations (1989), p. 235 | DOI:10.1007/978-3-642-61314-2_6
- Conclusion, The Book of Prime Number Records (1989), p. 347 | DOI:10.1007/978-1-4684-0507-1_8
- Adventures in arithmetick, or: How to make good use of a fourier transform, The Mathematical Intelligencer, Volume 9 (1987) no. 2, p. 53 | DOI:10.1007/bf03025900
- The Lore of Prime Numbers. By George P. Loweke, The American Mathematical Monthly, Volume 92 (1985) no. 9, p. 672 | DOI:10.1080/00029890.1985.11971712
- The Prime Number Theorem, Topics from the Theory of Numbers (1984), p. 169 | DOI:10.1007/978-0-8176-4838-1_9
- Elementary methods in the study of the distribution of prime numbers, Bulletin of the American Mathematical Society, Volume 7 (1982) no. 3, p. 553 | DOI:10.1090/s0273-0979-1982-15057-1
- References, Volume 58 (1974), p. 306 | DOI:10.1016/s0079-8169(08)60210-x
- A Simple Proof of a Theorem of Landau, Proceedings of the Edinburgh Mathematical Society, Volume 9 (1954) no. 2, p. 87 | DOI:10.1017/s0013091500021349
- XVIII.—The Elementary Proof of the Prime Number Theorem, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, Volume 63 (1952) no. 3, p. 257 | DOI:10.1017/s0080454100007135
- Neuer Beweis des Primzahlsatzes und Beweis des Primidealsatzes, Mathematische Annalen, Volume 56 (1903) no. 4, p. 645 | DOI:10.1007/bf01444310
- On some problems concerning the distribution of prime numbers., Bulletin de la Société Mathématique de France, Volume 28 (1900), pp. 25-38 | DOI:10.24033/bsmf.619 | Zbl:2665209
- On an application of Riemann's formula for the number of primes below a given limit., Journal für die Reine und Angewandte Mathematik, Volume 119 (1898), pp. 65-71 | DOI:10.1515/crll.1898.119.65 | Zbl:2670409
- On the zeros of the function
of Riemann, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, Volume 122 (1896), pp. 1470-1473 | Zbl:2675805
Cité par 126 documents. Sources : Crossref, zbMATH