An algebro-geometric study of special values of hypergeometric functions ${}_3F_2$

Masanori Asakura; Noriyuki Otsubo; Tomohide Terasoma

An algebro-geometric study of special values of hypergeometric functions ${}_3F_2$

Number Theory 2018-04-04 v2 Algebraic Geometry Classical Analysis and ODEs

Authors: Masanori Asakura , Noriyuki Otsubo , Tomohide Terasoma

Abstract

For certain class of hypergeometric functions ${}_3F_2$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.

Keywords

hypergeometric functions special values algebro-geometric study rational parameters logarithms of algebraic numbers higher regulators ${}_3F_2$

Cite

@article{arxiv.1603.04558,
  title  = {An algebro-geometric study of special values of hypergeometric functions ${}_3F_2$},
  author = {Masanori Asakura and Noriyuki Otsubo and Tomohide Terasoma},
  journal= {arXiv preprint arXiv:1603.04558},
  year   = {2018}
}

Comments

11 pages. The title was changed from "An algebro-geometric study of the unit arguments ${}_3F_2(1,1,q;a,b;1)$, I"

An algebro-geometric study of special values of hypergeometric functions ${}_3F_2$

Abstract

Keywords

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