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arXiv · 1503.07962

CM periods, CM regulators and hypergeometric functions, I

Masanori Asakura·Noriyuki Otsubo
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Abstract

We study the $H^2$ of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain $K_1$-elements are written in terms of values of hypergeometric functions ${}_3F_2$, and we prove their non-vanishing.

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Masanori Asakura, Noriyuki Otsubo. 2015-03-27. CM periods, CM regulators and hypergeometric functions, I. https://arxiv.org/abs/1503.07962

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