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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Publicado: 2018
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v356_n10_p973_Kohen
http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n10_p973_Kohen
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_1631073X_v356_n10_p973_Kohen
record_format dspace
spelling paper:paper_1631073X_v356_n10_p973_Kohen2023-06-08T16:25:38Z 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 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 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v356_n10_p973_Kohen 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
title Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes
spellingShingle 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
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v356_n10_p973_Kohen
http://hdl.handle.net/20.500.12110/paper_1631073X_v356_n10_p973_Kohen
_version_ 1768545207973838848

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