Ramanujan's convolution sum twisted by Dirichlet characters

We find formulas for convolutions of sum of divisor functions twisted by the Dirichlet character (−4/∗), which are analogous to Ramanujan's formula for convolution of usual sum of divisor functions. We use the theory of modular forms to prove our results.

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Main Authors:	Aygin, Zafer Selcuk, Hong, Nankun
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2021
Subjects:	Science::Mathematics Dedekind Eta Function Eisenstein Series
Online Access:	https://hdl.handle.net/10356/151108
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-1511082021-07-29T11:12:07Z Ramanujan's convolution sum twisted by Dirichlet characters Aygin, Zafer Selcuk Hong, Nankun School of Physical and Mathematical Sciences Science::Mathematics Dedekind Eta Function Eisenstein Series We find formulas for convolutions of sum of divisor functions twisted by the Dirichlet character (−4/∗), which are analogous to Ramanujan's formula for convolution of usual sum of divisor functions. We use the theory of modular forms to prove our results. Ministry of Education (MOE) The first author was supported by the Singapore Ministry of Education Academic Research Fund, Tier 2, project number MOE2014-T2-1-051, ARC40/14. 2021-07-29T11:12:07Z 2021-07-29T11:12:07Z 2019 Journal Article Aygin, Z. S. & Hong, N. (2019). Ramanujan's convolution sum twisted by Dirichlet characters. International Journal of Number Theory, 15(1), 137-152. https://dx.doi.org/10.1142/S1793042119500027 1793-0421 https://hdl.handle.net/10356/151108 10.1142/S1793042119500027 2-s2.0-85053326680 1 15 137 152 en MOE2014-T2-1-051 ARC40/14 International Journal of Number Theory © 2019 World Scientific Publishing Company. All rights reserved.
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Science::Mathematics Dedekind Eta Function Eisenstein Series
spellingShingle	Science::Mathematics Dedekind Eta Function Eisenstein Series Aygin, Zafer Selcuk Hong, Nankun Ramanujan's convolution sum twisted by Dirichlet characters
description	We find formulas for convolutions of sum of divisor functions twisted by the Dirichlet character (−4/∗), which are analogous to Ramanujan's formula for convolution of usual sum of divisor functions. We use the theory of modular forms to prove our results.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Aygin, Zafer Selcuk Hong, Nankun
format	Article
author	Aygin, Zafer Selcuk Hong, Nankun
author_sort	Aygin, Zafer Selcuk
title	Ramanujan's convolution sum twisted by Dirichlet characters
title_short	Ramanujan's convolution sum twisted by Dirichlet characters
title_full	Ramanujan's convolution sum twisted by Dirichlet characters
title_fullStr	Ramanujan's convolution sum twisted by Dirichlet characters
title_full_unstemmed	Ramanujan's convolution sum twisted by Dirichlet characters
title_sort	ramanujan's convolution sum twisted by dirichlet characters
publishDate	2021
url	https://hdl.handle.net/10356/151108
_version_	1707050442407542784

Ramanujan's convolution sum twisted by Dirichlet characters

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