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)

 

Bilinear sums with exponential functions


Author: Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 137 (2009), 2217-2224
MSC (2000): Primary 11L07, 11L26
Published electronically: March 4, 2009
MathSciNet review: 2495254
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ g\ne 0, \pm 1$ be a fixed integer. Given two sequences of complex numbers $ \left(\varphi_m\right)_{m=1}^\infty$ and $ \left(\psi_n\right)_{n=1}^\infty $ and two sufficiently large integers $ M$ and $ N$, we estimate the exponential sums

$\displaystyle \sum_{\substack{p \le M \\ \mathrm{gcd}(ag,p) =1}} \sum_{1 \le n \le N} \varphi_p\psi_n \mathbf{e}_p\left(a g^n\right), \qquad a \in \mathbb{Z}, $

where the outer summation is taken over all primes $ p \le M$ with $ \mathrm{gcd}(ag,p) =1$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11L07, 11L26

Retrieve articles in all journals with MSC (2000): 11L07, 11L26


Additional Information

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email: igor@ics.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09882-7
PII: S 0002-9939(09)09882-7
Received by editor(s): September 17, 2008
Published electronically: March 4, 2009
Additional Notes: During the preparation of this paper, the author was supported in part by ARC grant No. DP0556431.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.