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    Sign changes of Kloosterman sums and exceptional characters

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    We prove that the existence of exceptional real zeroes of Dirichlet LL-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 nn 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

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    We investigate the boundness of the Riesz transform on LpL^p for connected sum of manifolds where the Riesz transform is bounded on LpL^p
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