A new construction of \({\mathfrak p}\)-adic L-functions attached to certain elliptic curves with complex multiplication
type: Item
instance of: scholarly article
title: A new construction of \({\mathfrak p}\)-adic L-functions attached to certain elliptic curves with complex multiplication
zbMATH Open document ID: 0608.14015
author: John L. Boxall
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74738
review text: Although there now exists a vast literature on the p-adic L-functions attached to primes of ordinary reduction of an elliptic curve E, few works have been concerned with the case of supersingular primes. In this paper, the author restricts to the case of complex multiplications, and constructs a one-variable p-adic L-function in both cases, under a standard assumption on the field generated by the torsion points of E. The construction is based on interpolation of Eisenstein series. It would be interesting to compare the p-adic period occuring in this method with those given by Hodge-Tate theory. The article is complemented by a p-adic analogue of the Kronecker limit formula, and by a study of the L- functions having a pole at \(s=0\).
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14K22
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 3983358
zbMATH Keywords: p-adic L-functions
zbMATH Keywords: elliptic curve
zbMATH Keywords: supersingular primes
zbMATH Keywords: complex multiplications
zbMATH Keywords: interpolation of Eisenstein series
zbMATH Keywords: Kronecker limit formula
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
OpenAlex ID: W2332934493
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DOI: 10.5802/AIF.1068
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3983358