This article relates the Gross-Zagier formula with a simpler formula of Gross for special values of L-series, via the theory of congruences between modular forms. Given two modular forms f and g (of different levels) which are congruent but whose functional equations have sign - 1 and 1 respectively, and an imaginary quadratic field K satisfying certain auxiliary conditions, the main result gives a congruence between the algebraic part of L′(f/K, 1) (expressed in terms of Heegner points) and the algebraic part of the special value L(g/K, 1). Congruences of this type were anticipated by Jochnowitz, and for this reason are referred to as "Jochnowitz congruences.".
Euler systems and Jochnowitz congruences / M. Bertolini, H. Darmon. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - 121:2(1999), pp. 259-281.
|Titolo:||Euler systems and Jochnowitz congruences|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||1999|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1353/ajm.1999.0010|
|Appare nelle tipologie:||01 - Articolo su periodico|