Rankin--Eisenstein classes for modular forms
Number Theory
2021-01-27 v2
Abstract
In this paper we make a systematic study of certain motivic cohomology classes ("Rankin-Eisenstein classes") attached to the Rankin--Selberg convolution of two modular forms of weight . The main result is the computation of the -adic syntomic regulators of these classes. As a consequence we prove many cases of the Perrin-Riou conjecture for Rankin--Selberg convolutions of cusp forms.
Keywords
Cite
@article{arxiv.1501.03289,
title = {Rankin--Eisenstein classes for modular forms},
author = {Guido Kings and David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:1501.03289},
year = {2021}
}
Comments
Updated version with minor corrections. To appear in Amer. J. Math