@article{CM_1991__80_3_337_0, author = {Lichtin, Ben}, title = {On the moderate growth of generalized {Dirichlet} series for hypoelliptic polynomials}, journal = {Compositio Mathematica}, pages = {337--354}, publisher = {Kluwer Academic Publishers}, volume = {80}, number = {3}, year = {1991}, mrnumber = {1134260}, zbl = {0759.11027}, language = {en}, url = {http://www.numdam.org/item/CM_1991__80_3_337_0/} }
TY - JOUR AU - Lichtin, Ben TI - On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials JO - Compositio Mathematica PY - 1991 SP - 337 EP - 354 VL - 80 IS - 3 PB - Kluwer Academic Publishers UR - http://www.numdam.org/item/CM_1991__80_3_337_0/ LA - en ID - CM_1991__80_3_337_0 ER -
Lichtin, Ben. On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials. Compositio Mathematica, Tome 80 (1991) no. 3, pp. 337-354. http://www.numdam.org/item/CM_1991__80_3_337_0/
[A-S] Representations of integers by positive definite forms over arithmetic progressions, Il. J. of Math. 24 (1980), 612-618. | MR | Zbl
and :[Be] The analytic continuation of generalized functions with respect to a parameter, Functional Analysis and Applications 6 (1972), 26-40. | MR | Zbl
:[Bo] Zeta functions and Green's functions for linear partial differential operators of elliptic type with constant coefficients, Ann. of Math. 57 (1953), 32-56. | MR | Zbl
:[Ch-Na] Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. of Math. 76 (1962), 93-136. | MR | Zbl
and :[Ep] Zur Theorie Allgemeiner Zetafunctionen, Math. Annalen 56 (1903), 615-644. | JFM | MR
:[H-R] The general theory of Dirichlet's series, Hafner Publishing Co., 1972.
and :[Ho] Analysis of linear partial differential operators II, Grundlehren, vol. 257, Springer-Verlag, 1983. | MR | Zbl
:[La] Über die Anzahl der Gitterpunkte in gewissen Bereichen (Zweite Abhandlung), Kgl. Ges. d. Wiss. Nachrichten. Math-Phys. Klasse. (Göttingen) 2 (1915), 209-243. | JFM
:[Li-1] Generalized Dirichlet series and b-functions, Comp. Math. 65 (1988), 81-120. | Numdam | MR | Zbl
:[Li-2] Poles of Dirichlet series and D-modules, Théorie des Nombres, Comptes rendus de la Conférence international de Théorie des Nombres tenue à I'Université Laval, 1987, pp. 579-594. | MR | Zbl
:[Li-3] The asymptotics of a lattice point problem associated to finitely many polynomials I, Duke J. of Math. (to appear). | Zbl
:[Li-4] The asymptotics of a lattice point problem determined by a hypoelliptic polynomial (submitted to Proceedings of Conference on D-modules and Microlocal Geometry, held in Lisbon, Portugal 1990). | Zbl
:[Sa-1] Prolongement meromorphe des séries de Dirichlet associées á des fractions rationelles de plusieurs variables, Ann. Inst. Fourier 33 (1984), 82-123. | Numdam | MR | Zbl
:[Sa-2] Croissance de certaines séries de Dirichlet et applications, J. reine und ang. Math. 367 (1986), 139-154. | MR | Zbl
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