A note on Kronecker's double sum and non-holomorphic Eisenstein series

SHEN Li-chien

doi:10.3969/j.issn.1000-5641.2018.03.001

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May 2018

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SHEN Li-chien. A note on Kronecker's double sum and non-holomorphic Eisenstein series[J]. Journal of East China Normal University (Natural Sciences), 2018, (3): 1-17. doi: 10.3969/j.issn.1000-5641.2018.03.001

Citation:

SHEN Li-chien. A note on Kronecker's double sum and non-holomorphic Eisenstein series[J]. Journal of East China Normal University (Natural Sciences), 2018, (3): 1-17. doi: 10.3969/j.issn.1000-5641.2018.03.001

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A note on Kronecker's double sum and non-holomorphic Eisenstein series

doi: 10.3969/j.issn.1000-5641.2018.03.001

SHEN Li-chien

Department of Mathematics, University of Florida, Gainesville FL 32611-8105, USA

Received Date: 2017-09-11
Publish Date: 2018-05-25

Abstract

Abstract

A family of non-holomorphic Eisenstein series of weight k and level N is generated from twisting of the Kronecker double series by Dirichlet characters and from which we will derive its representation in terms of the Whittaker function and the functional equation for the Eisenstein series.
- Dirichlet character,
- conductor,
- Gaussian sum,
- twisted Poisson summation formula,
- Whittaker function

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References(6)

References

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[5]	WEIL A. Elliptic Functions According to Eisenstein and Kronecker[M]. Berlin:Springer-Verlag, 1976.
[6]	WHITTAKER E T, WATSON G N. A Course of Modern Analysis[M]. 4th ed. Cambridge:Cambridge University Press, 1958.