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TERNARY DIVISOR FUNCTIONS IN ARITHMETIC PROGRESSIONS TO SMOOTH MODULI

Part of: Multiplicative number theory Finite fields and commutative rings (number-theoretic aspects) Exponential sums and character sums Sequences and sets

Published online by Cambridge University Press:  19 June 2018

Ping Xi
Ping Xi*
Affiliation:
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China email ping.xi@xjtu.edu.cn
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Abstract

We prove that the exponent of distribution of $\unicode[STIX]{x1D70F}_{3}$ in arithmetic progressions can be as large as $\frac{1}{2}+\frac{1}{34}$, provided that the moduli is squarefree and has only sufficiently small prime factors. The tools involve arithmetic exponent pairs for algebraic trace functions, as well as a double $q$-analogue of the van der Corput method for smooth bilinear forms.

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions 11N25: Distribution of integers with specified multiplicative constraints 11B25: Arithmetic progressions 11T23: Exponential sums 11L05: Gauss and Kloosterman sums; generalizations
Type
Research Article
Information
Mathematika , Volume 64 , Issue 3 , 2018 , pp. 701 - 729
Copyright
Copyright © University College London 2018 

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