Universität zu Köln

Ehlen, Stephan ORCID: 0000-0003-2029-6219, Guerzhoy, Pavel, Kane, Ben and Rolen, Larry (2020). Central L-values of elliptic curves and local polynomials. Proc. London Math. Soc., 120 (5). S. 742 - 770. HOBOKEN: WILEY. ISSN 1460-244X

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Abstract

Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of L-functions. In particular, we find a criterion for vanishing of certain twisted central L-values of a family of elliptic curves, whereby vanishing occurs precisely when the values of two finite sums over canonical binary quadratic forms coincide. This yields a vanishing criterion based on vastly simpler formulas than the formulas related to work of Birch and Swinnerton-Dyer to determine such L-values, and extends beyond their framework to special non-CM elliptic curves.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ehlen, Stephan UNSPECIFIED orcid.org/0000-0003-2029-6219 UNSPECIFIED Guerzhoy, Pavel UNSPECIFIED UNSPECIFIED UNSPECIFIED Kane, Ben UNSPECIFIED UNSPECIFIED UNSPECIFIED Rolen, Larry UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-335806
DOI:	10.1112/plms.12305
Journal or Publication Title:	Proc. London Math. Soc.
Volume:	120
Number:	5
Page Range:	S. 742 - 770
Date:	2020
Publisher:	WILEY
Place of Publication:	HOBOKEN
ISSN:	1460-244X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MODULAR-FORMS; FOURIER COEFFICIENTS; CONJECTURE Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/33580