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On the zeros of certain Epstein zeta functions
Citation Information: Forum Mathematicum. Volume 20, Issue 2, Pages 359–385, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.018, May 2008
- Published Online:
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.
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