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Averages of shifted convolutions of d3(n)

Part of: Additive number theory; partitions Multiplicative number theory Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  12 April 2012

S. Baier ,
T. D. Browning ,
G. Marasingha  and
L. Zhao
S. Baier
Affiliation:
Mathematisches Institut, Universität Göttingen, Bunsenstrasse 3–5, 37073 Göttingen, Germany (sbaier@uni-math.gwdg.de)
T. D. Browning
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK (t.d.browning@bristol.ac.uk; gihan.marasingha@bristol.ac.uk)
G. Marasingha
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK (t.d.browning@bristol.ac.uk; gihan.marasingha@bristol.ac.uk)
L. Zhao
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore (lzhao@pmail.ntu.edu.sg)
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Abstract

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We investigate the first and second moments of shifted convolutions of the generalized divisor function d3(n).

Keywords

divisor functionconvolution sumsmoments of Riemann zeta functionHardy–Littlewood circle method

MSC classification

Secondary: 11N37: Asymptotic results on arithmetic functions 11M06: $zeta (s)$ and $L(s, chi)$ 11P55: Applications of the Hardy-Littlewood method

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 551 - 576
Copyright
Copyright © Edinburgh Mathematical Society 2012

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