Relations de Manin d'ordre 2 vérifiées par le polynôme des bi-périodes d'un couple de formes modulaires

2017/10/01 by Nicolas Provost, Provost, Nicolas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1710.00412

openalex publication_date 2017/10/01 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

Manin's relations characterize period polynomials of a modular form. In this paper, we propose a finite set of relations checked by bi-period polynomials of a couple of forms. Then we construct an Eisenstein part of depth 2 which essentially completed the set of bi-periods polynomials among polynomials canceled by the relations. By giving a computational description of that part, we prove a result of irrationality of ratio of the periods for some weights.

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