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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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 |
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1768545207973838848 |