Classical automorphic forms and hypergeometric functions
type: Item
instance of: scholarly article
title: Classical automorphic forms and hypergeometric functions
zbMATH Open document ID: 0644.10019
DOI: 10.1016/0022-314X(88)90067-4
author: Peter F. Stiller
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: The author exhibits a graded algebra of hypergeometric functions and shows how to canonically identify it with the graded algebra of modular forms for the full modular group SL(2,\({\mathbb{Z}})\). He also shows how Dedekind's eta-function is related to the square root of a hypergeometric function and gives yet another simple proof of its functional equation.
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4049718
zbMATH Keywords: Mellin transforms
zbMATH Keywords: special values of Dirichlet series
zbMATH Keywords: integrals of hypergeometric functions
zbMATH Keywords: graded algebra of hypergeometric functions
zbMATH Keywords: graded algebra of modular forms
zbMATH Keywords: Dedekind's eta-function
zbMATH Keywords: functional equation
MaRDI profile type: Publication
cites work: Q5824493
cites work: Q4157010
cites work: Q5268866
cites work: A simple proof of η(— 1/τ)= η(τ)√τ/i
cites work: Special values of Dirichlet series, monodromy, and the periods of automorphic forms
cites work: A Note on Automorphic Forms of Weight One and Weight Three
cites work: A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
description: scientific article; zbMATH DE number 4049718