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2017 Distinguished-root formulas for generalized Calabi–Yau hypersurfaces
Alan Adolphson, Steven Sperber
Algebra Number Theory 11(6): 1317-1356 (2017). DOI: 10.2140/ant.2017.11.1317

Abstract

By a “generalized Calabi–Yau hypersurface” we mean a hypersurface in n of degree d dividing n + 1. The zeta function of a generic such hypersurface has a reciprocal root distinguished by minimal p-divisibility. We study the p-adic variation of that distinguished root in a family and show that it equals the product of an appropriate power of p times a product of special values of a certain p-adic analytic function . That function is the p-adic analytic continuation of the ratio F(Λ)F(Λp), where F(Λ) is a solution of the A-hypergeometric system of differential equations corresponding to the Picard–Fuchs equation of the family.

Citation

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Alan Adolphson. Steven Sperber. "Distinguished-root formulas for generalized Calabi–Yau hypersurfaces." Algebra Number Theory 11 (6) 1317 - 1356, 2017. https://doi.org/10.2140/ant.2017.11.1317

Information

Received: 30 March 2016; Revised: 20 February 2017; Accepted: 21 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06763328
MathSciNet: MR3687099
Digital Object Identifier: 10.2140/ant.2017.11.1317

Subjects:
Primary: 11G25
Secondary: 14G15

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 6 • 2017
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