Rankin-Eisenstein classes for modular forms

Rankin-Eisenstein classes for modular forms

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 $\ge 2$. The main result is the computation of the $p$-adic syntomic regulators of these classes. As a co...

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Veröffentlicht in:American journal of mathematics 2020-02, Vol.142 (1), p.79
Hauptverfasser: Kings, Guido, Loeffler, David, Zerbes, Sarah Livia
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Convolution
Homology
Regulators
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Zusammenfassung: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 $\ge 2$. The main result is the computation of the $p$-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.
ISSN:0002-9327
1080-6377
DOI:10.1353/ajm.2020.0002