# Number Theory, Strings, and Quantum Physics

31 May 2021 to 5 June 2021
Online
Asia/Tokyo timezone

## A Whipple formula revisited

1 Jun 2021, 09:00
1h 15m
Online

#### Online

Organized by Kavli IPMU

### Speaker

Ling Long (Louisiana State U.)

### Description

A well-known formula of Whipple relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)$. In this paper we revisit this relation from the viewpoint of the underlying hypergeometric data $HD$, to which there are also associated hypergeometric character sums and Galois representations. We explain a special structure behind Whipple's formula when the hypergeometric data $HD$ are primitive and defined over rationals. As a consequence, the values of the corresponding hypergeometric character sums can be explicitly expressed in terms of Fourier coefficients of certain modular forms. We further relate the hypergeometric values $_7F_6(1)$ in Whipple's formula to the periods of modular forms.

### Presentation Materials

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