Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Applications of a theorem of H. Cramér to the Selberg class
HTML articles powered by AMS MathViewer

by J. Kaczorowski and A. Perelli PDF
Proc. Amer. Math. Soc. 130 (2002), 2821-2826 Request permission

Abstract:

We prove two results on the nature of the Dirichlet coefficients $a(n)$ of the $L$-functions in the extended Selberg class $\mathcal {S}^\sharp$. The first result asserts that if $a(n)=\phi (\log n)$ for some entire function $\phi (z)$ of order 1 and finite type, then $\phi (z)$ is constant. The second result states, roughly, that if $a(n)\phi (\log n)$ are still the coefficients of some $L$-function from $\mathcal {S}^\sharp$, then $\phi (z)=ce^{i\beta z}$ with $c\in \mathbb {C}$ and $\beta \in \mathbb {R}$. The proofs are based on an old result by Cramér and on the characterization of the functions of degree 1 of $\mathcal {S}^\sharp$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11M41
  • Retrieve articles in all journals with MSC (2000): 11M41
Additional Information
  • J. Kaczorowski
  • Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, 60-769 Poznań, Poland
  • MR Author ID: 96610
  • Email: kjerzy@math.amu.edu.pl
  • A. Perelli
  • Affiliation: Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy
  • MR Author ID: 137910
  • Email: perelli@dima.unige.it
  • Received by editor(s): May 11, 2001
  • Published electronically: April 17, 2002
  • Communicated by: Dennis A. Hejhal
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 2821-2826
  • MSC (2000): Primary 11M41
  • DOI: https://doi.org/10.1090/S0002-9939-02-06542-5
  • MathSciNet review: 1908263