Determination of elliptic curves by their adjoint p-adic L-functions

Maria Monica Nastasescu

doi:10.1016/j.jnt.2014.12.012

Determination of elliptic curves by their adjoint p-adic L-functions

Maria Monica Nastasescu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Fix p an odd prime. Let E be an elliptic curve over Q with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E. To do this, we prove a result on the determination of isobaric representations of GL(3,AQ) by certain L-values of p-power twists.

Original language	English (US)
Pages (from-to)	156-181
Number of pages	26
Journal	Journal of Number Theory
Volume	152
DOIs	https://doi.org/10.1016/j.jnt.2014.12.012
State	Published - Jul 1 2015

Keywords

Elliptic curve
L-function
P-adic L-function

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2014.12.012

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title = "Determination of elliptic curves by their adjoint p-adic L-functions",

abstract = "Fix p an odd prime. Let E be an elliptic curve over Q with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E. To do this, we prove a result on the determination of isobaric representations of GL(3,AQ) by certain L-values of p-power twists.",

keywords = "Elliptic curve, L-function, P-adic L-function",

author = "Nastasescu, {Maria Monica}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

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language = "English (US)",

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AU - Nastasescu, Maria Monica

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N2 - Fix p an odd prime. Let E be an elliptic curve over Q with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E. To do this, we prove a result on the determination of isobaric representations of GL(3,AQ) by certain L-values of p-power twists.

AB - Fix p an odd prime. Let E be an elliptic curve over Q with semistable reduction at p. We show that the adjoint p-adic L-function of E evaluated at infinitely many integers prime to p completely determines up to a quadratic twist the isogeny class of E. To do this, we prove a result on the determination of isobaric representations of GL(3,AQ) by certain L-values of p-power twists.

KW - Elliptic curve

KW - L-function

KW - P-adic L-function

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DO - 10.1016/j.jnt.2014.12.012

M3 - Article

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SP - 156

EP - 181

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

Determination of elliptic curves by their adjoint p-adic L-functions

Abstract

Keywords

ASJC Scopus subject areas

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