Convolution and square in abelian groups II

Yves Benoist (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 Université Paris-Saclay

A critical value on an abelian group G of odd order d is a value λ such that the functional equation f⋆f (2 t) = λf (t)^2 on G has a nonzero solution f. We construct many critical values by using abelian varieties with complex multiplication.

Mots clés: 2020 Math. subject class. Primary 11F03; Secondary 11F27 Functional Equation; Convolution; Abelian variety; Torsion groups; Complex multiplication; Theta functions; Weil number; Modular variety

Domaines: Géométrie algébrique [math.AG]

Yves Benoist. Convolution and square in abelian groups II. 2022. ⟨hal-03744506⟩