Titlebook: Geometry, Algebra, Number Theory, and Their Information Technology Applications; Toronto, Canada, Jun Amir Akbary,Sanoli Gun Conference pro

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Manfred Wick,Wulf Pinggera,Paul LehmannLet . be a . Hecke cusp form, and let . be a primitive Dirichlet character modulo ., which we assume to be prime. We prove the Burgess-type bound for the twisted .-function: .The method also yields the original bound of Burgess for Dirichlet .-functions:

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https://doi.org/10.1007/978-3-7091-5141-9We introduce a new technique for sieving over smooth moduli in the higher-rank Selberg sieve and obtain asymptotic formulas for the same.

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Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial ArThe value of sums of the type .where . is a linear polynomial, a quadratic irreducible polynomial, a sequence connected with primes, etc., has been largely studied. We give here a first result concerning the distribution modulo 1 of such sequences for the case of polynomials of arbitrary degree.

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A Smooth Selberg Sieve and Applications,We introduce a new technique for sieving over smooth moduli in the higher-rank Selberg sieve and obtain asymptotic formulas for the same.

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