Sign changes of Kloosterman sums and exceptional characters
Résumé
We prove that the existence of exceptional real zeroes of Dirichlet $L$-functions would lead to cancellations in the sum $\sum_{p\leq x} \Kl(1, p)$ of Kloosterman sums over primes, and also to sign changes of ${\rm Kl}(1, n)$, where $n$ runs over integers with exactly two prime factors. Our arguments involve a variant of Bombieri's sieve, bounds for twisted sums of Kloosterman sums, and work of Fouvry and Michel on sums of $\left| {\rm Kl}(1, n)\right|$.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...