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

2018/01/04 by Daniel Kohen, Kohen, Daniel, Ariel Pacetti +2
Arts and Humanities · Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Primary: 11G05 #Secondary: 11G40 #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1801.01619

openalex publication_date 2018/01/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let E be a rational elliptic curve and let p be an odd prime of additive\nreduction. Let K be an imaginary quadratic field and fix a positive integer\nc prime to the conductor of E. The main goal of the present article is to\ndefine an anticyclotomic p-adic L-function L attached to E/K when\nE/ QQ_p attains semistable reduction over an abelian extension. We prove that\n L satisfies the expected interpolation properties; namely, we show that if\n\χ is an anticyclotomic character of conductor cpⁿ then \χ( L) is\nequal (up to explicit constants) to L(E,\χ,1) or L'(E,\χ,1).\n

Citations

• Iwasawa Theory for Elliptic Curves at Unstable Primes

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