Distribution of Difference between Inverses of Consecutive Integers modulo P

Distribution of Modular Inverses and Multiples of Small Integers and the Sato–Tate Conjecture on Average

We show that, for sufficiently large integers m and X, for almost all a = 1,. .. , m the ratios a/x and the products ax, where |x| X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average over r and s, ranging over relatively short intervals, the distribution of Kloosterman sums K r,s (...

Distribution of Inverses and Multiples of Small Integers and the Sato–Tate Conjecture on Average

We show that, for sufficiently large integers m and X, for almost all a = 1,. .. , m the ratios a/x and the products ax, where |x| X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average over r and s, ranging over relatively short intervals, the distribution of Kloosterman sums K r,s (...

On the Consecutive Powers of a Primitive Root: Gaps and Exponential Sums

For a primitive root g modulo a prime p ≥ 1 we obtain upper bounds on the gaps between the residues modulo p of the N consecutive powers agn , n = 1, . . . , N , which is uniform over all integers a with gcd(a, p)= 1. §

On Inversion in Z_{2^n-1}

In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z2n−1, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function Invd (n), which for a fixed positive integer d maps integers n ≥ 1 to the least positive residue of the inverse of d modulo 2n − 1, if it exists. In particular, we showe...

On the Distribution of Inverses Modulo n