Distribution of Inverses and Multiples of Small Integers and the Sato–Tate Conjecture on Average
نویسنده
چکیده
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 (p) = p−1 n=1 exp(2πi(rn + sn −1)/p), for primes p T is in accordance with the Sato–Tate conjecture.
منابع مشابه
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 (...
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