Email this article Double Character Sums with Intervals and Arbitrary Sets
- Authors: Shkredov I.D.1,2,3, Shparlinski I.E.4
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Institute for Information Transmission Problems (Kharkevich Institute)
- Moscow Institute of Physics and Technology (State University)
- Department of Pure Mathematics
- Issue: Vol 303, No 1 (2018)
- Pages: 239-258
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175686
- DOI: https://doi.org/10.1134/S0081543818080199
- ID: 175686
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Abstract
We obtain a new bound on certain double sums of multiplicative characters which improves several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical object of study in additive combinatorics.
About the authors
Ilya D. Shkredov
Steklov Mathematical Institute of Russian Academy of Sciences; Institute for Information Transmission Problems (Kharkevich Institute); Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: ilya.shkredov@gmail.com
Russian Federation, ul. Gubkina 8, Moscow, 119991; Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051; Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701
Igor E. Shparlinski
Department of Pure Mathematics
Author for correspondence.
Email: igor.shparlinski@unsw.edu.au
Australia, Sydney, NSW, 2052
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