Abstract
We give simple proofs of the essential properties of the Beurling–Selberg function and its odd part by viewing them as solutions to difference equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. C. Baker, Diophantine Inequalities, London Mathematical Society Monographs 1, Oxford University Press (1986).
P. T. Bateman and H. Diamond, Analytic Number Theory, World Scientific Publishing Co. (2007).
H. Cohen, Number Theory, Volume II, Graduate Texts in Mathematics 240, Springer-Verlag (2007).
M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Lecture Notes in Mathematics 1651, Springer-Verlag (1997).
J. Friedlander and H. Iwaniec, Opera de Cribro, Colloquium Publications 57, American Mathematical Society (2010).
H. L. Montgomery, The analytic principle of the large sieve, Bull. Amer. Math. Soc., 84 (1978), 547–567.
A. Selberg, Atle Selberg Collected Papers, Volume II, Springer-Verlag (1991).
G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics 46, Cambridge University Press (1995).
J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc., 12 (1985), 183–216.
Author information
Authors and Affiliations
Corresponding author
Additional information
Corresponding author.
Rights and permissions
About this article
Cite this article
Akhilesh, P., Ramana, D.S. A remark on the Beurling–Selberg function. Acta Math Hung 139, 354–362 (2013). https://doi.org/10.1007/s10474-012-0277-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-012-0277-5