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Averages of point configuration problems over finite p-adic rings.
- Source :
- Proceedings of the American Mathematical Society; Jul2021, Vol. 149 Issue 7, p2825-2839, 15p
- Publication Year :
- 2021
-
Abstract
- This paper studies averages of finite point configuration problems for subsets E ⊂ (Z/p<superscript>r</superscript>)<superscript>n</superscript> (r ≥ 1, n ≥ 2) and extends work of Bennett-Hart-Iosevich-Pakianathan-Rudnev over finite fields to finite p-adic rings. As a result, we show that averages, taken over the group of orthogonal transformations, of finite point configurations with endpoints in E are positive if the density of E is sufficiently large. [ABSTRACT FROM AUTHOR]
- Subjects :
- FINITE rings
FINITE fields
TRANSFORMATION groups
EXPONENTIAL sums
FOURIER transforms
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 150284299
- Full Text :
- https://doi.org/10.1090/proc/15449