Supercongruences of Atkin and Swinnerton-Dyer type for Legendre polynomials
type: Item
instance of: scholarly article
title: Supercongruences of Atkin and Swinnerton-Dyer type for Legendre polynomials
zbMATH Open document ID: 0732.11021
DOI: 10.1016/0022-314X(91)90019-8
author: N. E. Zubov
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: Mit dem Titel der Arbeit sind Kongruenzen modulo bestimmter Primpotenzen für gewisse spezielle Werte von Legendrepolynomen gemeint. Diese treten als Entwicklungskoeffizienten holomorpher Differentiale elliptischer Kurven auf. Die Kongruenzen sind vor allem im Fall komplexer Multiplikation interessant und werden mit Hilfe virtuoser Rechnungen abgeleitet, die vor allem die Weierstraßsche \(\wp\)-Funktion, klassische Thetafunktionen und ihre Transformationsformeln benutzen.
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11G15
Mathematics Subject Classification ID: 14K25
zbMATH DE Number: 4210238
zbMATH Keywords: congruences
zbMATH Keywords: complex multiplication
zbMATH Keywords: elliptic functions
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: Weierstrass p-function
zbMATH Keywords: theta function
zbMATH Keywords: transformation formula
reviewed by: Jürgen Wolfart
MaRDI profile type: Publication
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full work available at URL: 0022-314x(91)90019-8
OpenAlex ID: W2084699162
description: scientific article; zbMATH DE number 4210238