Modular regulators and multiple Eisenstein values

François Brunault; Wadim Zudilin

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arXiv · 2303.15554

Modular regulators and multiple Eisenstein values

François Brunault·Wadim Zudilin

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Abstract

We introduce a new methodology for length reduction of multiple modular values as developed by Brown; it involves an interpolation of multiple Eisenstein values and differentiation with respect to their continuous elliptic parameters. We apply our method to computing explicitly the Goncharov regulator integral associated to $K_4$ classes on modular curves in terms of $L$-values of modular forms. We use this expression to connect it with the Beilinson regulator integral. Our general approach reveals new interesting arithmetic phenomena and prospects for the general $K$-groups of modular curves.

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François Brunault, Wadim Zudilin. 2023-03-27. Modular regulators and multiple Eisenstein values. https://arxiv.org/abs/2303.15554

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