The shifted convolution of generalized divisor functions

by Berke Topacogullari
Doctoral thesis
Date of Examination:2016-08-22
Date of issue:2017-04-18
Advisor:Prof. Dr. Valentin Blomer
Referee:Prof. Dr. Valentin Blomer
Referee:Prof. Dr. Jörg Brüdern
Persistent Address: http://dx.doi.org/10.53846/goediss-6257

 

 

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Abstract

English

We prove an asymptotic formula for the shifted convolution of the divisor functions \(d_k(n)\) and \(d(n)\) with \(k \geq 3\), which is uniform in the shift parameter and which has a power saving error term. Along the way, we also consider a few other variants of the shifted convolution problem.
Keywords: divisor functions; shifted convolution sums; additive divisor problems
 
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