The Kloosterman sums on the ellipse
Copyright policy )The Kloosterman sums on the ellipse
The main point of our research is to obtain the estimates for Kloosterman sums K(α, β; h, q; k) considered on the ellipse bound for the case of the integer rational moduleq and forsome natural number k with conditions (α, q)=(β, q)=1 on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function τℓ(α)forℓ= 2,3, . . . over the ring of integer elements of imaginary quadratic field in arithmetic progression.
imaginary quadratic field, Exponential sums, Estimates on exponential sums, Gauss and Kloosterman sums; generalizations, exponential sums, asymptotic formulas, Kloosterman sums
imaginary quadratic field, Exponential sums, Estimates on exponential sums, Gauss and Kloosterman sums; generalizations, exponential sums, asymptotic formulas, Kloosterman sums
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