Distance and sum–product problems over finite   p  ‐adic rings | Zendy

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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

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.

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