This article is cited in 20 papers

Arithmetic hypergeometric series

W. Zudilin

School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, Australia

Abstract: The main goal of this survey is to give common characteristics of auxiliary hypergeometric functions (and their generalisations), functions which occur in number-theoretic problems. Originally designed as a tool for solving these problems, the hypergeometric series have become a connecting link between different areas of number theory and mathematics in general.
Bibliography: 183 titles.

Keywords: hypergeometric series, zeta value, Ramanujan's mathematics, Diophantine approximation, irrationality measure, modular form, Calabi–Yau differential equation, Mahler measure, Wilf–Zeilberger theory, algorithm of creative telescoping.

UDC: 511+517

MSC: Primary 33C20; Secondary 05A19, 11B65, 11F11, 11J82, 11M06, 11Y60, 14H52

Received: 18.02.2011

DOI: 10.4213/rm9420

 English version: Russian Mathematical Surveys, 2011, 66:2, 369–420

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