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

Abstract

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

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

References in corpus (2)

• Polyharmonic Maass forms for PSL(2, Z)
• Modular invariants for real quadratic fields and Kloosterman sums