648,149 research outputs found
Sign changes of Kloosterman sums and exceptional characters
We prove that the existence of exceptional real zeroes of Dirichlet
-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 \Kl(1, n), where
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| \Kl(1, n)\right|.Comment: 11 page
Riesz transforms on connected sums
We investigate the boundness of the Riesz transform on for connected
sum of manifolds where the Riesz transform is bounded on
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