Uniform Titchmarsh divisor problems
نویسندگان
چکیده
Asymptotic formulae for Titchmarsh-type divisor sums are obtained with strong error terms that uniform in the shift parameter. This applies to more general arithmetic functions such as of two squares, improving term representation number a sum prime and Fourier coefficients cusp forms, generalizing result Pitt.
منابع مشابه
Generalizing the Titchmarsh Divisor Problem
Let a be a natural number different from 0. In 1963, Linnik proved the following unconditional result about the Titchmarsh divisor problem ∑ p≤x d(p− a) = cx + O ( x log log x log x ) where c is a constant dependent on a. Titchmarsh proved the above result assuming GRH for Dirichlet L-functions in 1931. We establish the following asymptotic relation: ∑ p≤x p≡a mod k d ( p− a k ) = Ckx + O ( x l...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2021
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2021.108076