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Distance and sum–product problems over finite p ‐adic rings
Author(s) -
Lichtin Ben
Publication year - 2019
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12219
Subject(s) - mathematics , finite field , product (mathematics) , exponential function , covert , ring (chemistry) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , geometry , linguistics , philosophy , chemistry , organic chemistry
Abstract This paper uses p ‐adic analytic and exponential sum (mod p ) estimates to solve distance and sum–product type problems for subsets of( Z / p r ) 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.