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arXiv · 2509.19960

Linear relations between $L$-values of newforms and moments of elliptic $K$ integral

Kam Cheong Au
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Abstract

By systematically translating certain integrals involving moments of the elliptic integral into $L$-values of modular forms on $\Gamma_1(4), \Gamma(4)$ and $\Gamma_1(8)$, and then utilizing relations among the critical $L$-values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals.

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Kam Cheong Au. 2025-09-24. Linear relations between $L$-values of newforms and moments of elliptic $K$ integral. https://arxiv.org/abs/2509.19960

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