Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The group ring of $ \mathbb{Q}/\mathbb{Z}$ 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
Published electronically: October 21, 2008
MathSciNet review: 2465650
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: First we prove some elementary but useful identities in the group ring of $ \mathbb{Q}/\mathbb{Z}$. 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11N25, 11B57

Retrieve articles in all journals with MSC (2000): 11N25, 11B57


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: http://dx.doi.org/10.1090/S0002-9939-08-09624-X
PII: S 0002-9939(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.