Formes automorphes et theoremes de Riemann-Roch arithmetiques

TL;DR

This paper constructs three families of automorphic forms using the arithmetic Riemann-Roch theorem and Lefschetz formula, revealing the arithmetic origin of two previously known families by Yoshikawa.

Contribution

It introduces a new construction method for automorphic forms based on arithmetic geometry, clarifying the arithmetic nature of existing families.

Findings

Two families match Yoshikawa's constructions

The third family is newly constructed

The approach links automorphic forms to arithmetic geometry

Abstract

Nous construisons trois familles de formes automorphes au moyen du theoreme de Riemann-Roch arithmetique et de la formule de Lefschetz arithmetique. Deux de ces familles ont deja ete construites par Yoshikawa et notre construction met en lumiere leur origine arithmetique. ----- We construct three families of automorphic forms following the arithmetic Riemann-Roch theorem and the arithmetic Lefschetz formula. Two of these families were already constructed by Yoshikawa and our construction illuminates their arithmetic origin.