The asymptotic distribution of Kloosterman sums

On the Distribution of Kloosterman Sums

For a prime p, we consider Kloosterman sums Kp(a) = ∑ x∈F p exp(2πi(x + ax)/p), a ∈ Fp, over a finite field of p elements. It is well known that due to results of Deligne, Katz and Sarnak, the distribution of the sums Kp(a) when a runs through Fp is in accordance with the Sato–Tate conjecture. Here we show that the same holds where a runs through the sums a = u+v for u ∈ U , v ∈ V for any two s...

The Asymptotic Distribution of Exponential Sums, I

On the Asymptotic Distribution of Certain Sums

On zeros of Kloosterman sums

The Value 4 of Binary Kloosterman Sums

Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory. Very recently Mesnager has showed that the value 4 of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension. In this paper we analyze the different...