紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2014, 51(2), p. 425-438

ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL

Watanabe, Humihiko

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-04

The Wirtinger integral is the uniformization to the upper half plane H of the hypergeometric function defined on the complex projective line P^1. In [5] we established the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → -1/τ with the aide of the theory of theta functions. As a corollary we obtain the transformation formulas of the Wirtinger integral for the linear fractional transformations τ → τ + 2 and τ → τ/(-2τ + 1) which are identified with generators of the principal congruence subgroup Γ(2) modulo center. These formulas correspond to the monodromy matrices of the hypergeometric function for generators of the fundamental group of P^1 minus three points. The purpose of this paper is to generalize this result, that is, we establish the transformation formula of the Wirtinger integral for a general element (a b c d) of Γ (2), which corresponds to a general monodromy matrix of the hypergeometric function.

10.18910/29198

29198

ON THE GENERAL TRANSFORMATION OF THE WIRTINGER INTEGRAL

Watanabe, Humihiko

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-04

Osaka Journal of Mathematics

51

2

425

438

https://hdl.handle.net/11094/29198

10.18910/29198

https://doi.org/10.18910/29198