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October 2016 Integrals on $p$-adic upper half planes and Hida families over totally real fields
Isao Ishikawa
Osaka J. Math. 53(4): 1089-1124 (October 2016).

Abstract

Bertolini--Darmon and Mok proved a formula of the second derivative of the two-variable $p$-adic $L$-function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some $p$-adic logarithm map. The theory of $p$-adic indefinite integrals and $p$-adic multiplicative integrals on $p$-adic upper half planes plays an important role in their work. In this paper, we generalize these integrals for $p$-adic measures which are not necessarily $\mathbb{Z}$-valued, and prove a formula of the second derivative of the two-variable $p$-adic $L$-function of an abelian variety of $\mathrm{GL}(2)$-type associated to a Hilbert modular form of weight 2.

Citation

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Isao Ishikawa. "Integrals on $p$-adic upper half planes and Hida families over totally real fields." Osaka J. Math. 53 (4) 1089 - 1124, October 2016.

Information

Published: October 2016
First available in Project Euclid: 4 October 2016

zbMATH: 06654666
MathSciNet: MR3554859

Subjects:
Primary: 11F41, 11G10, 11S40

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics

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Vol.53 • No. 4 • October 2016
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