Incomplete Character Sums and Applications

Thursday, October 2, 2014 - 3:15pm - 4:05pm
Keller 3-180
Mei-Chu Chang (University of California)
In the talk, we survey various results on incomplete multiplicative character sums obtained over recent years and some of their applications. The relation with sum-product goes back as far as Vinogradov's shifted product technique and Burgess work. Methods from arithmetic combinatorics and geometry of numbers play a role in extending Burgess results to various multi-dimensional settings but unfortunately did not allow to break the 1/4 threshold so far. We also discuss a unified treatment of the Graham-Ringrose and Postnikov argument for very short
character sums when the modulus has only small prime factors and give an application to integral points on Markoff-Hurwitz and Dwork hypersurfaces.
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