Some Ω-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem
Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 1, pp. 41-50.

Nous donnons des estimations de type Ω relatives au terme reste dans la formule asymptotique pour le moment d’ordre quatre de la fonction zêta de Riemann et au terme reste dans le problème des diviseurs.

We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.

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     title = {Some $\Omega $-results related to the fourth power moment of the {Riemann} zeta-function and to the additive divisor problem},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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     year = {1997},
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Kaczorowski, Jerzy; Szydło, Bogdan. Some $\Omega $-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem. Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 1, pp. 41-50. https://www.numdam.org/item/JTNB_1997__9_1_41_0/

[1] R.J. Anderson, H.M. Stark, Oscillation theorems, Analytic Number Theory, LNM 899, Springer-Verlag, Berlin 1981, 79-106. | MR | Zbl

[2] J.-M. Deshouillers, H. Iwaniec, Additive divisor problem, J. London Math. Soc., 26(2), (1982), 1-14. | MR | Zbl

[3] A. Ivić, Y. Motohashi, On the fourth power moment of the Riemann zeta-function, J. Number Theory 51(1995), 16-45. | MR | Zbl

[4] A. Ivić, Y. Motohashi, The mean square of the error term for the fourth moment of the zeta-function, Proc. London Math. Soc. (3)69(1994), 309-329. | MR | Zbl

[5] M. Jutila, The additive divisor problem and exponential sums, Proc. Third Conf. Canadian Number Theory Association (Kingston 1991), Clarendon Press, Oxford 1993, 113-135. | MR | Zbl

[6] J. Kaczorowski, Results on the distribution of primes, J. reine angew. Math., 446(1994), 89-113. | MR | Zbl

[7] E. Landau, Ueber einen Satz von Tschebyschef, Math. Ann. 61(1905), 527-550. | JFM | MR

[8] Y. Motohashi, Spectral mean values of Maass waveform L-functions, J. Number Th. 42(1992), 258-284. | MR | Zbl

[9] Y. Motohashi, The binary additive divisor problem, Ann Sci. L'Ecole Norm. Sup., 27(4)(1994), 529-572. | Numdam | MR | Zbl

[10] Y. Motohashi, A relation between the Riemann zeta-function and the hyperbolic Laplacian, Ann. Sc. Norm. Sup. Pisa Cl. Sci., 22(4)(1995), 299-313. | Numdam | MR | Zbl

[11] B. Szydlo, On oscillations in the additive divisor problem, I, Acta Arith., 66(1994), 63-69. | MR | Zbl

[12] L.A. Tahtadjan, A.I. Vinogradov, The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian, Zap. Nauch. Sem. LOMI, ANSSSR 134, (1984), 84-116, (Russian). | MR | Zbl