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arXiv · 1309.6021

Rational exponential sums over the divisor function

Bryce Kerr
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Abstract

We consider a problem posed by Shparlinski, of giving nontrivial bounds for rational exponential sums over the arithmetic function $τ(n)$, counting the number of divisors of $n$. This is done using some ideas of Sathe concerning the distribution in residue classes of the function $ω(n)$, counting the number of prime factors of $n$, to bring the problem into a form where, for general modulus, we may apply a bound of Bourgain concerning exponential sums over subgroups of finite abelian groups and for prime modulus some results of Korobov and Shkredov.

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Bryce Kerr. 2013-09-24. Rational exponential sums over the divisor function. https://arxiv.org/abs/1309.6021

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