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

2018/03/21 by Cormac O’Sullivan, O'Sullivan, Cormac
Mathematics · #11F30 #11F37 #11M06 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.08210

openalex publication_date 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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