The group ring of and an application of a divisor problem

Authors:
Alan K. Haynes and Kosuke Homma

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1285-1293

MSC (2000):
Primary 11N25, 11B57

DOI:
https://doi.org/10.1090/S0002-9939-08-09624-X

Published electronically:
October 21, 2008

MathSciNet review:
2465650

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Abstract | References | Similar Articles | Additional Information

Abstract: First we prove some elementary but useful identities in the group ring of . Our identities have potential applications to several unsolved problems which involve sums of Farey fractions. In this paper we use these identities, together with some analytic number theory and results about divisors in short intervals, to estimate the cardinality of a class of sets of fundamental interest.

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Additional Information

**Alan K. Haynes**

Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom

Email:
akh502@york.ac.uk

**Kosuke Homma**

Affiliation:
Department of Mathematics, University of Texas, Austin, Texas 78712

Email:
khomma@math.utexas.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09624-X

Keywords:
Farey fractions,
circle group,
divisors

Received by editor(s):
March 24, 2008

Received by editor(s) in revised form:
May 1, 2008

Published electronically:
October 21, 2008

Additional Notes:
The research of the first author was supported by EPSRC grant EP/F027028/1

Communicated by:
Ken Ono

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.