Moments and equidistributions of multiplicative analogues of Kloosterman sums

Seventh Power Moments of Kloosterman Sums

Evaluations of the n-th power moments Sn of Kloosterman sums are known only for n 6 6. We present here substantial evidence for an evaluation of S7 in terms of Hecke eigenvalues for a weight 3 newform on Γ0(525) with quartic nebentypus of conductor 105. We also prove some congruences modulo 3, 5 and 7 for the closely related quantity T7, where Tn is a sum of traces of n-th symmetric powers of t...

Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums

Abstract. In this paper, we construct two binary linear codes associated with multi-dimensional and m−multiple power Kloosterman sums (for any fixed m) over the finite field Fq. Here q is a power of two. The former codes are dual to a subcode of the binary hyper-Kloosterman code. Then we obtain two recursive formulas for the power moments of multi-dimensional Kloosterman sums and for the m-mult...

Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals

We investigate the solubility of the congruence xy ≡ 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.

Second Moments of Dirichlet L-functions Weighted by Kloosterman Sums

Simple Recursive Formulas Generating Power Moments of Kloosterman Sums

In this paper, we construct four binary linear codes closely connected with certain exponential sums over the finite field Fq and Fq − {0, 1}. Here q is a power of two. Then we obtain four recursive formulas for the power moments of Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of the ...