For the Gauss sums which are defined by Sn(a, q) := ∑

We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.

is again a Dirichlet character modulo n. In fact, the set of Dirichlet characters modulo n is again a multiplicative group, called the dual group of (Z/nZ)× and denoted ̂ (Z/nZ)×. The identity element of the dual group, mapping every element of (Z/nZ)× to 1, is the trivial character modulo n, denoted 1n or just 1 when n is clear, Since (Z/nZ)× is a finite group the values taken by any Dirichlet ...

I describe the use of NMR experiments which implement Gauss sums as a method for factoring numbers and discuss whether this approach can be computationally useful.

Abstract The main purpose of this article is by using the properties fourth character modulo a prime p and analytic methods to study calculating problem certain hybrid power mean involving two-term exponential sums reciprocal quartic Gauss sums, give some interesting formulae them.

We explore further the hardness of the non-dual discrete variant of the Ring-LWE problem for various number rings, give improved attacks for certain rings satisfying some additional assumptions, construct a new family of vulnerable Galois number fields, and apply some number theoretic results on Gauss sums to deduce the likely failure of these attacks for 2-power cyclotomic rings and unramified...

We give an explicit construction of circulant graphs of very high energy. This construction is based on Gauss sums. We also show the Littlewood conjecture can be used to establish new result for a certain class of circulant graphs. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50; 11T24; 42A05