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Pré-Publication, Document De Travail Année : 2022

The mixing conjecture under GRH

Valentin Blomer
  • Fonction : Auteur
Ilya Khayutin
  • Fonction : Auteur

Résumé

We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in rational quaternion algebras. The proof is conditional on the Generalized Riemann Hypothesis, and when the division algebra is indefinite we furthermore assume the Ramanujan conjecture. Our methods, which provide an effective rate, are based on the spectral theory of automorphic forms and their $L$-functions, as well as techniques in classical analytic number theory.

Dates et versions

hal-03913417 , version 1 (26-12-2022)

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Valentin Blomer, Farrell Brumley, Ilya Khayutin. The mixing conjecture under GRH. 2022. ⟨hal-03913417⟩
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