Large even order character sums
HTML articles powered by AMS MathViewer
- by Leo Goldmakher and Youness Lamzouri PDF
- Proc. Amer. Math. Soc. 142 (2014), 2609-2614 Request permission
Abstract:
A classical theorem of Paley asserts the existence of an infinite family of quadratic characters whose character sums become exceptionally large. In this paper, we establish an analogous result for characters of any fixed even order. Previously our bounds were only known under the assumption of the Generalized Riemann Hypothesis.References
- Harold Davenport, Multiplicative number theory, 3rd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York, 2000. Revised and with a preface by Hugh L. Montgomery. MR 1790423
- Leo Goldmakher, Multiplicative mimicry and improvements to the Pólya-Vinogradov inequality, Algebra Number Theory 6 (2012), no. 1, 123–163. MR 2950162, DOI 10.2140/ant.2012.6.123
- Leo Goldmakher and Youness Lamzouri, Lower bounds on odd order character sums, Int. Math. Res. Not. IMRN 21 (2012), 5006–5013. MR 2993442, DOI 10.1093/imrn/rnr219
- Andrew Granville and K. Soundararajan, Large character sums: pretentious characters and the Pólya-Vinogradov theorem, J. Amer. Math. Soc. 20 (2007), no. 2, 357–384. MR 2276774, DOI 10.1090/S0894-0347-06-00536-4
- H. L. Montgomery and R. C. Vaughan, Exponential sums with multiplicative coefficients, Invent. Math. 43 (1977), no. 1, 69–82. MR 457371, DOI 10.1007/BF01390204
- Hugh L. Montgomery and Robert C. Vaughan, Multiplicative number theory. I. Classical theory, Cambridge Studies in Advanced Mathematics, vol. 97, Cambridge University Press, Cambridge, 2007. MR 2378655
- R. E. A. C. Paley, A Theorem on Characters, J. London Math. Soc. 7 (1932), no. 1, 28–32. MR 1574456, DOI 10.1112/jlms/s1-7.1.28
Additional Information
- Leo Goldmakher
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Email: lgoldmak@math.toronto.edu
- Youness Lamzouri
- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada
- MR Author ID: 804642
- Email: lamzouri@mathstat.yorku.ca
- Received by editor(s): May 15, 2012
- Received by editor(s) in revised form: May 17, 2012, and August 19, 2012
- Published electronically: April 8, 2014
- Additional Notes: The first author was partially supported by an NSERC Discovery Grant
- Communicated by: Matthew A. Papanikolas
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 2609-2614
- MSC (2010): Primary 11L40
- DOI: https://doi.org/10.1090/S0002-9939-2014-11990-3
- MathSciNet review: 3209316