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

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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.

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Acknowledgements

Support for this project was provided by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York.

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  1. Dept. of Math, The CUNY Graduate Center, 365 Fifth Avenue, New York, NY, 10016-4309, USA

    Cormac O’Sullivan

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O’Sullivan, C. Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers. Res. number theory 4, 36 (2018). https://doi.org/10.1007/s40993-018-0129-7

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