Distance and sum-product problems over finite p-adic rings

被引：2

作者：

Lichtin, Ben ^{[1
]}

机构：

[1] 49 Boardman St, Rochester, NY 14607 USA

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2019年 / 118卷 / 06期

关键词：

11T24; 52C10 (primary);

D O I：

10.1112/plms.12219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper uses p-adic analytic and exponential sum (mod p) estimates to solve distance and sum-product type problems for subsets of (Z/pr)n (r > 1,n > 2). In doing so, we improve upon earlier results of Covert-Iosevich-Pakianathan and extend earlier work of Hart-Iosevich-Solymosi from finite fields to finite p-adic rings.

引用

页码：1450 / 1470

页数：21

共 11 条

[1] Covert D, 2012, INDIANA U MATH J, V61, P1949
[2] Dabrowski R, 1997, ACTA ARITH, V80, P1
[3] Deligne P., 1974, I HAUTES ETUDES SCI, V43, P273, DOI 10.1007/BF02684373
[4] Sum-product Estimates in Finite Fields via Kloosterman Sums
Hart, Derrick
Iosevich, Alex
Solymosi, Jozsef
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2007, 2007
[5] Igusa J.-I., 1978, TATA I LECT, V59
[6] Erdos distance problem in vector spaces over finite fields
Iosevich, A.
Rudnev, M.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (12) : 6127 - 6142
[7] Katz NM, 1999, INT MATH RES NOTICES, V1999, P875
[8] On a question of Heath-Brown: Good estimates on average for higher degree Kloosterman sums
Lichtin, B
[J]. FORUM MATHEMATICUM, 2003, 15 (03) : 329 - 375
[9] About Kloosterman's sums S(u,v,q)
Salie, H
[J]. MATHEMATISCHE ZEITSCHRIFT, 1932, 34 : 91 - 109
[10] Tao Terence, 2009, Contrib. Discrete Math., V4, P59

← 1 2 →