Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes

Let E be a rational elliptic curve and let p be an odd prime of additive reduction. Let K be an imaginary quadratic field and fix a positive integer c prime to the conductor of E. The main goal of the present article is to define an anticyclotomic p-adic L-function L attached to E/K when E/Qp attain...

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Autores principales: Kohen, D., Pacetti, A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n10_p973_Kohen
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_1631073X_v356_n10_p973_Kohen
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spelling todo:paper_1631073X_v356_n10_p973_Kohen2023-10-03T16:28:36Z Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes Kohen, D. Pacetti, A. Let E be a rational elliptic curve and let p be an odd prime of additive reduction. Let K be an imaginary quadratic field and fix a positive integer c prime to the conductor of E. The main goal of the present article is to define an anticyclotomic p-adic L-function L attached to E/K when E/Qp attains semistable reduction over an abelian extension. We prove that L satisfies the expected interpolation properties; namely, we show that if χ is an anticyclotomic character of conductor cpn, then χ(L) is equal (up to explicit constants) to L(E,χ,1) or L′(E,χ,1). © 2018 Académie des sciences JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n10_p973_Kohen
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Let E be a rational elliptic curve and let p be an odd prime of additive reduction. Let K be an imaginary quadratic field and fix a positive integer c prime to the conductor of E. The main goal of the present article is to define an anticyclotomic p-adic L-function L attached to E/K when E/Qp attains semistable reduction over an abelian extension. We prove that L satisfies the expected interpolation properties; namely, we show that if χ is an anticyclotomic character of conductor cpn, then χ(L) is equal (up to explicit constants) to L(E,χ,1) or L′(E,χ,1). © 2018 Académie des sciences
format JOUR
author Kohen, D.
Pacetti, A.
spellingShingle Kohen, D.
Pacetti, A.
Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
author_facet Kohen, D.
Pacetti, A.
author_sort Kohen, D.
title Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
title_short Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
title_full Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
title_fullStr Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
title_full_unstemmed Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
title_sort anticyclotomic p-adic l-functions for elliptic curves at some additive reduction primes
url http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n10_p973_Kohen
work_keys_str_mv AT kohend anticyclotomicpadiclfunctionsforellipticcurvesatsomeadditivereductionprimes
AT pacettia anticyclotomicpadiclfunctionsforellipticcurvesatsomeadditivereductionprimes
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