English

Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers

Number Theory 2018-10-23 v2

Abstract

New expressions are given for the Fourier expansions of non-holomorphic Eisenstein series with weight kk. Among other applications, this leads to non-holomorphic analogs of formulas of Ramanujan, Grosswald and Berndt containing Eichler integrals of holomorphic Eisenstein series.

Keywords

Cite

@article{arxiv.1803.08210,
  title  = {Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers},
  author = {Cormac O'Sullivan},
  journal= {arXiv preprint arXiv:1803.08210},
  year   = {2018}
}

Comments

33 pages, 2 figures, minor corrections and improvements, appearing in Res. Number Theory