Premium
Simultaneous diagonal p –adic equations
Author(s) -
Meir I. D.
Publication year - 1998
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014248
Subject(s) - mathematics , diagonal , degree (music) , pure mathematics , mathematical analysis , geometry , acoustics , physics
It is known that a system of r additive equations of degree k with greater than 2 rk variables has a non‐trivial p ‐adic solution for all p > k 2 r + 2 . In this paper we consider the same system with more than crk variables, c > 2, and show the existence of a non‐trivial solution for all p > r 2 k 2+(2/( c − 2)) if r ≠ 1 and p > k 2+(2/( c − 1)) if r = 1.