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arXiv · 2108.00840

Semi-modular forms from Fibonacci-Eisenstein series

A. P. Akande·Robert Schneider
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Abstract

In recent work, M. Just and the second author defined a class of "semi-modular forms" on $\mathbb C$, in analogy with classical modular forms, that are "half modular" in a particular sense; and constructed families of such functions as Eisenstein-like series using symmetries related to integer partitions. Looking for further natural examples of semi-modular behavior, here we construct a family of Eisenstein-like series to produce semi-modular forms, using symmetries related to Fibonacci numbers instead of partitions. We then consider other Lucas sequences that yield semi-modular forms.

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A. P. Akande, Robert Schneider. 2021-08-02. Semi-modular forms from Fibonacci-Eisenstein series. https://arxiv.org/abs/2108.00840

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