Zero-Density Estimates for Epstein Zeta Functions*

Autor:	Steven M. Gonek, Yoonbok Lee
Rok vydání:	2016
Předmět:	Pure mathematics General Mathematics 010102 general mathematics Zero (complex analysis) Sigma Positive-definite matrix Term (logic) Quadratic form (statistics) 01 natural sciences Upper and lower bounds 010101 applied mathematics Asymptotic formula 0101 mathematics Class number Mathematics
Zdroj:	The Quarterly Journal of Mathematics. 68:301-344
ISSN:	1464-3847 0033-5606
DOI:	10.1093/qmath/haw041
Popis:	We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients in the vertical strip $\sigma_\mathit1\mathit \il \mathfrak Rs\mathit \lt \sigma_\mathit2$ , where $1/2\lt \sigma_1\lt \sigma_2 \lt$ . When the class number of the quadratic form is bigger than 1, Voronin gives a lower bound and Lee gives an asymptotic formula for the number of zeros. In this paper, we improve their results by providing a new upper bound for the error term.
Databáze:	OpenAIRE
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