ON HEILBRONN'S EXPONENTIAL SUM

Mordell’s Exponential Sum Estimate Revisited

Bilinear Exponential Sums and Sum-Product Problems on Elliptic Curves

Let E be an ordinary elliptic curve over a finite field IFq of q elements. We improve a bound on bilinear additive character sums over points on E, and obtain its analogue for bilinear multiplicative character sums. We apply these bounds to some variants of the sum-product problem on E. 2000 Mathematics Subject Classification: Primary 11G05, 11L07, 11T23

On Least Squares Exponential Sum Approximation With Positive Coefficients*

An algorithm is given for finding optimal least squares exponential sum approximations to sampled data subject to the constraint that the coefficients appearing in the exponential sum are positive. The algorithm employs the divided differences of exponentials to overcome certain problems of ill-conditioning and is suitable for data sampled at noninteger times.

On the Exponential Sum over K - Free Numbersj

Bounds on an exponential sum arising in Boolean circuit complexity

We study exponential sums of the form S = 2−n ∑x∈{0,1}n em(h(x))eq(p(x)), where m,q ∈ Z+ are relatively prime, p is a polynomial with coefficients in Zq , and h(x)= a(x1 + · · · + xn) for some 1 a < m. We prove an upper bound of the form 2−Ω(n) on |S|. This generalizes a result of J. Bourgain, who establishes this bound in the case where q is odd. This bound has consequences in Boolean circuit ...