Affiliation:
1. Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México Morelia México
2. School of Mathematics and Statistics University of New South Wales Sydney Australia
Abstract
AbstractFor a prime number p and integer x with , let denote the multiplicative inverse of x modulo p. In this paper, we are interested in the problem of distribution modulo p of the sequence
and in lower bound estimates for the corresponding exponential sums. As representative examples, we state the following two consequences of the main results.For any fixed and for any sufficiently large integer N, there exists a prime number p with
such that
For any fixed positive , there exists a positive constant c such that the following holds: for any sufficiently large integer N there is a prime number such that
and
Funder
Australian Research Council