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August 2020 Alternative summation orders for the Eisenstein series $G_2$ and Weierstrass $\wp$-function
Dan Romik, Robert Scherer
Rocky Mountain J. Math. 50(4): 1473-1482 (August 2020). DOI: 10.1216/rmj.2020.50.1473

Abstract

We consider alternative orders of summation for the conditionally convergent series defining the weight-2 Eisenstein series G2 and the Weierstrass -function. The resulting sums differ from the standard ones by a residual term that can be thought of as a function of the shapes with respect to which we sum. We compute this residual function explicitly and give some examples. The results generalize the well-known quasimodularity relationship between G2 and its series summed in the reverse order.

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Dan Romik. Robert Scherer. "Alternative summation orders for the Eisenstein series $G_2$ and Weierstrass $\wp$-function." Rocky Mountain J. Math. 50 (4) 1473 - 1482, August 2020. https://doi.org/10.1216/rmj.2020.50.1473

Information

Received: 19 November 2019; Revised: 10 January 2020; Accepted: 10 January 2020; Published: August 2020
First available in Project Euclid: 29 September 2020

zbMATH: 07261875
MathSciNet: MR4154818
Digital Object Identifier: 10.1216/rmj.2020.50.1473

Subjects:
Primary: 30B99, 40A05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 4 • August 2020
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