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arXiv · 1001.4496

Modular equations and lattice sums

Mathew Rogers·Boonrod Yuttanan
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Abstract

We highlight modular equations discovered by Somos and Ramanujan, and use them to prove new relations between lattice sums and hypergeometric functions. We also discuss progress towards solving Boyd's Mahler measure conjectures, and we conjecture a new formula for $L(E,2)$ of conductor 17 elliptic curves.

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Mathew Rogers, Boonrod Yuttanan. 2010-01-25. Modular equations and lattice sums. https://arxiv.org/abs/1001.4496

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