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Forum Mathematicum

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Volume 20, Issue 2 (Mar 2008)


On the zeros of certain Epstein zeta functions

Enrico Bombieri
  • Enrico Bombieri, Institute for Advanced Study, Princeton NJ 08540, USA.
  • Email:
/ Julia Mueller
  • Julia Mueller, Mathematics Department, Fordham University, 407 John Mulcahy Hall, Bronx, NY 10458-5165, USA.
Published Online: 2008-05-04 | DOI: https://doi.org/10.1515/FORUM.2008.018


This paper studies the distribution of zeros of certain Epstein zeta functions, associated to positive definite binary quadratic forms with class number 2, in the region of absolute convergence of their Dirichlet series. In particular, one obtains upper and lower bounds for the rate of approach of zeros to the boundary of the zero-free half-plane for such functions. The proof for the lower bound depends on Bohr's method for studying simultaneous diophantine approximations. The upper bound uses instead a deep result on the diophantine type of the ratio of the logarithms of two rational numbers.

2000 Mathematics Subject Classification: 11E45; 11M41.

About the article

Received: 2005-09-30

Published Online: 2008-05-04

Published in Print: 2008-03-01

Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.018. Export Citation

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