中文

关于临界线上Epstein zeta函数零点间空隙的注记

数论 2017-03-13 v2

摘要

证明了与正定整二元二次型相关的Epstein zeta函数ζQ(s)\zeta_{Q}(s)在充分大的正数TT下有一个零点1/2+iγ1/2 + i\gamma,满足TγT+T3/7+εT \leq \gamma \leq T + T^{{3/7} +\varepsilon}。这是对M. Jutila和K. Srinivas的结果(Bull. London Math. Soc. 37 (2005) 45--53)的改进。

关键词

引用

@article{arxiv.1602.06069,
  title  = {A note on the gaps between zeros of Epstein's zeta-functions on the critical line},
  author = {Stephan Baier and Srinivas Kotyada and Usha Keshav Sangale},
  journal= {arXiv preprint arXiv:1602.06069},
  year   = {2017}
}

备注

17 pages, major revisions, expanded version of the earlier draft, to appear in Functiones et Approximatio