%0 Journal Article
%T Small zeros of quadratic forms mod P^m
%A A. H. Hakami
%J International Mathematical Forum
%D 2013
%I 
%X Let $Q({bf{x}}) = Q(x_1 ,x_2 ,...,x_n )$ be aquadratic form over $mathbb{Z}$, $p$ be an odd prime, and $Delta= left( {( - 1)^{n/2} det A_Q /p} right)$. A solution of thecongruence $Q({mathbf{x}}) equiv {mathbf{0}};(bmod p^m )$ issaid to be a primitive solution if $pnmid x_i $ for some $i$. Weprove that if this congruence has a primitive solution then it has aprimitive solution with $left| {mathbf{x}} right| leqslantmax { 6^{1/n} p^{m[(1/2) + (1/n)]} ,2^{2(n + 1)/(n - 2)} 3^{2/(n -2)} } $.
%K Quadratic forms
%K congruences
%K small solutions
%U http://www.m-hikari.com/imf/imf-2013/5-8-2013/hakamiIMF5-8-2013.pdf