Some remarks on Fourier coefficients of Hecke modular functions

• Autorzy: Kaczorowski, J.
• Języki publikacji: EN

Abstrakty

EN

The main goal of the paper is to prove that the Hecke modular functions are in some sense rare objects. A geometric approach is applied. Two topologies in the space of complex sequences with polynomial growth are denned, and in both cases we prove that the set of Fourier coefficients of Hecke modular functions form a discrete subset. A quantitative version of this statement is also provided. The proof of the main result depends on non-linear twists of degree two L-functions.

Słowa kluczowe

EN

L-functions; Hecke modular functions; Fourier coefficients; non-linear twists

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 105-121
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Kaczorowski, J.

• Adam Mickiewicz University, Faculty of Mathematics and Computer Science, ul. Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• [1] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. I. McGraw-Hill, 1953.
• [2] E. Hecke, Lectures on Dirichlet Series, Modular Functions and Quadratic Forms, Göttingen, 1983.
• [3] J. Kaczorowski and A. Perelli, The Selberg class; a survey, Number Theory in Progress, Proc. Conf, in Honor of A. Schinzel, ed. by K. Györy et al., 953-992, de Gruyter, 1999.
• [4] J. Kaczorowski and A. Perelli, On the structure of the Selberg class, VI; non-linear twists, to appear in Acta Arithmetica, (2004).
• [5] E. C. Titchmarsh, The Theory of Functions, 2nd edition, Oxford, 1939.

Uwagi

Dedicated to Prof. Julian Musielak on his 75th birthday.