On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials

Ben Lichtin

Compositio Mathematica (1991)

  • Volume: 80, Issue: 3, page 337-354
  • ISSN: 0010-437X

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Lichtin, Ben. "On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials." Compositio Mathematica 80.3 (1991): 337-354. <http://eudml.org/doc/90128>.

@article{Lichtin1991,
author = {Lichtin, Ben},
journal = {Compositio Mathematica},
keywords = {generalized Dirichlet series; hypoelliptic polynomials; counting functions; -function; functional equations},
language = {eng},
number = {3},
pages = {337-354},
publisher = {Kluwer Academic Publishers},
title = {On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials},
url = {http://eudml.org/doc/90128},
volume = {80},
year = {1991},
}

TY - JOUR
AU - Lichtin, Ben
TI - On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 80
IS - 3
SP - 337
EP - 354
LA - eng
KW - generalized Dirichlet series; hypoelliptic polynomials; counting functions; -function; functional equations
UR - http://eudml.org/doc/90128
ER -

References

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  1. [A-S] C. An and A. Stein: Representations of integers by positive definite forms over arithmetic progressions, Il. J. of Math.24 (1980), 612-618. Zbl0428.10013MR586799
  2. [Be] J. Bernstein: The analytic continuation of generalized functions with respect to a parameter, Functional Analysis and Applications6 (1972), 26-40. Zbl0282.46038MR320735
  3. [Bo] S. Bochner: Zeta functions and Green's functions for linear partial differential operators of elliptic type with constant coefficients, Ann. of Math.57 (1953), 32-56. Zbl0050.08001MR54830
  4. [Ch-Na] K. Chandrasekharan and R. Narasimhan: Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. of Math.76 (1962), 93-136. Zbl0211.37901MR140491
  5. [Ep] P. Epstein: Zur Theorie Allgemeiner Zetafunctionen, Math. Annalen56 (1903), 615-644. Zbl34.0461.02MR1511190JFM34.0461.02
  6. [H-R] G.H. Hardy and M. Riesz: The general theory of Dirichlet's series, Hafner Publishing Co., 1972. Zbl45.0387.03
  7. [Ho] L. Hörmander: Analysis of linear partial differential operators II, Grundlehren, vol. 257, Springer-Verlag, 1983. Zbl0521.35002MR705278
  8. [La] E. Landau: Über die Anzahl der Gitterpunkte in gewissen Bereichen (Zweite Abhandlung), Kgl. Ges. d. Wiss. Nachrichten. Math-Phys. Klasse. (Göttingen) 2 (1915), 209-243. Zbl45.0312.02JFM45.0312.02
  9. [Li-1] B. Lichtin: Generalized Dirichlet series and b-functions, Comp. Math.65 (1988), 81-120. Zbl0637.32002MR930148
  10. [Li-2] B. Lichtin: 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. Zbl0699.10060MR1024589
  11. [Li-3] B. Lichtin: The asymptotics of a lattice point problem associated to finitely many polynomials I, Duke J. of Math. (to appear). Zbl0735.11048
  12. [Li-4] B. Lichtin: 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). Zbl0820.11061
  13. [Sa-1] P. Sargos: Prolongement meromorphe des séries de Dirichlet associées á des fractions rationelles de plusieurs variables, Ann. Inst. Fourier33 (1984), 82-123. Zbl0523.10026MR762695
  14. [Sa-2] P. Sargos: Croissance de certaines séries de Dirichlet et applications, J. reine und ang. Math.367 (1986), 139-154. Zbl0575.10035MR839128

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