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2018 , Vol. 2018 >Issue 3: 1 - 17

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.03.001

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

  • SHEN Li-chien
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  • Department of Mathematics, University of Florida, Gainesville FL 32611-8105, USA

Received date: 2017-09-11

  Online published: 2018-05-29

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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.

Key words： Dirichlet character; conductor; Gaussian sum; twisted Poisson summation formula; Whittaker function

Cite this article

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

References

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[6] WHITTAKER E T, WATSON G N. A Course of Modern Analysis[M]. 4th ed. Cambridge:Cambridge University Press, 1958.
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