Construction of automorphic forms and integrals-Reference-Cited by-同舟云学术

Construction of automorphic forms and integrals

Published:1974 Issue:0 Volume:191 Page:373-385
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Niebur Douglas

Abstract

It is well known that modular forms of positive dimension have Fourier coefficients given by certain infinite series involving Kloostermann sums and the modified Bessel function of the first kind. In this paper a functional equation which characterizes all such Fourier series is found. It is also shown that these Fourier series have a construction similar to that of Poincaré series of negative dimension.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1974-191-00/S0002-9947-1974-0344196-8/S0002-9947-1974-0344196-8.pdf

Reference6 articles.

1. Construction of automorphic forms on 𝐻-groups and supplementary Fourier series;Knopp, Marvin Isadore;Trans. Amer. Math. Soc.,1962

2. Mathematical Surveys, No. VIII;Lehner, Joseph,1964

3. Zur analytischen Theorie der Grenzkreisgruppen;Petersson, Hans;Math. Ann.,1938

4. Hans Rademacher, On the partition function 𝑝(𝑛), Proc. London Math. Soc. (2) 43 (1937), 241-254.

5. The Fourier Series and the Functional Equation of the Absolute Modular Invariant J(𝜏);Rademacher, Hans;Amer. J. Math.,1939

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