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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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 |
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R-134 |
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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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1807324258604417024 |