Twisted Dirichlet series and distributions

Paul Gérardin; Wen-Ch'ing Winnie Li

Compositio Mathematica (1990)

  • Volume: 73, Issue: 3, page 271-293
  • ISSN: 0010-437X

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Gérardin, Paul, and Li, Wen-Ch'ing Winnie. "Twisted Dirichlet series and distributions." Compositio Mathematica 73.3 (1990): 271-293. <http://eudml.org/doc/90006>.

@article{Gérardin1990,
author = {Gérardin, Paul, Li, Wen-Ch'ing Winnie},
journal = {Compositio Mathematica},
keywords = {tempered distribution; generalization of Hamburger's theorem; Dirichlet series; S-integers; global field; summation formula; quasicharacters},
language = {eng},
number = {3},
pages = {271-293},
publisher = {Kluwer Academic Publishers},
title = {Twisted Dirichlet series and distributions},
url = {http://eudml.org/doc/90006},
volume = {73},
year = {1990},
}

TY - JOUR
AU - Gérardin, Paul
AU - Li, Wen-Ch'ing Winnie
TI - Twisted Dirichlet series and distributions
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 73
IS - 3
SP - 271
EP - 293
LA - eng
KW - tempered distribution; generalization of Hamburger's theorem; Dirichlet series; S-integers; global field; summation formula; quasicharacters
UR - http://eudml.org/doc/90006
ER -

References

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  2. [B-C] S. Bochner and K. Chandrasekharan, On Riemann functional equation, Ann. of Math.63 (1956) 336-359. Zbl0071.06601MR79034
  3. [Br] F. Bruhat, Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes p-adiques, Bull. Soc. Math. de France89 (1961), 43-75. Zbl0128.35701MR140941
  4. [G-S] I.M. Gelfand and G.E. Shilov, Generalized Functions I, Academic Press, 1954. Zbl0115.33101
  5. [G-L] P. Gérardin and W.-C.W. Li: Functional equations and periodic sequences, in Théorie des Nombres, Comptes Rendus de la Conférence internationale de Théorie des nombres tenue à l'Université Laval en 1987, Ed. J.M. De Koninck et C. Levesque, de Gruyter, 1989, 267-279. Zbl0688.10039MR1024568
  6. [Ha] H. Hamburger, Uber die Riemannsche Funktionalgleichung der ζ-Funktion, Math. Zeit.10 (1921), 240-254. Zbl48.1210.03JFM48.1210.03
  7. [He] E. Hecke, Uber die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann.112 (1936), 664-699. Zbl0014.01601MR1513069
  8. [J-L] H. Jacquet and R.P. Langlands, Automorphic Forms on GL(2), Lecture Notes in Mathematics114, Springer-Verlag, 1970. Zbl0236.12010MR401654
  9. [K-M] J.-P. Kahane and S. Mandelbrojt, Sur l'équation fonctionnelle de Riemann et la formule sommatoire de Poisson, Ann. Sc. Ec. Norm. Sup. (3) 75 (1958), 57-80. Zbl0086.06004MR106208
  10. [L] W.-C.W. Li, On converse theorems for GL(2) and GL(1), Amer. J. Math.103 (1981) 851-885. Zbl0477.12013MR630770
  11. [S] L. Schwartz, Théorie des Distributions, Hermann, Paris, 1957. Zbl0149.09501MR209834
  12. [Si] C.L. Siegel, Bemerkung zu eine Satz von Hamburger uber die Funktionalgleichung der Riemannscher zeta-Funktion, Math. Ann.86 (1922), 276-279. MR1512091JFM48.1216.01
  13. [T] J. Tate, Fourier analysis in number fields and Hecke's zeta functions, Thesis, Princeton University (May 1950); published in Algebraic Number Theory, Cassels and Frohlich ed., Academic Press1976, 305-347. MR217026
  14. [V] M.-F. Vignéras, Facteurs gamma et équations fonctionnelles, in Modular Functions in One Variable VI, Lecture Notes in Mathematics, 627, Springer-Verlag, 1977, 79-103. Zbl0373.10027MR485739
  15. [W 1] A. Weil, Fonctions zeta et distributions, in Oeuvres Scientifiques - Collected Papers, vol. III, Springer-Verlag, 1980, 158-163. 
  16. [W 2] A. Weil, Basic Number Theory, Springer-Verlag, 1967. Zbl0176.33601MR234930

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