In this volume we have endeavored to provide a middle ground-hopefully even a bridge-
between" theory" and" experiment" in the matter of prime numbers. Of course, we speak of …

There has been a great deal of interest lately in studying rings in which every element can
be written as a sum of potent elements and nilpotent elements. In this paper, we focus …

We show that the Waring number over a finite field F q, denoted as g (k, q), when exists
coincides with the diameter of the generalized Paley graph Γ (k, q)= C ay (F q, R k) with R …

We prove some bounds on incomplete additive character sums of polynomials over finite
fields. We also apply results on incomplete additive character sums to get a distribution …

Deterministic algorithms are presented for the efficient solution of diagonal homogeneous
equations in many variables over finite fields. As auxiliary algorithms, it is shown how to …

In this paper we obtain explicit results for Waring's problem over general finite rings,
especially matrix rings over finite fields by building on analogous results over finite fields …

We consider a special class of generalized Paley graphs over finite fields, namely the
Cayley graphs with vertex set Fqm and connection set the nonzero (qℓ+ 1)-th powers in …

Let p be a prime, n be an integer, k| pn–1, and γ (k, pn) be the minimal value of s such that
every number in 𝔽 pn is a sum of sk th powers. A known upper bound is improved to γ (k …

Bent functions are maximally nonlinear Boolean functions. They are wonderful creatures
introduced by O. Rothaus in the 1960's and studied firstly by J. Dillon since 1974. Using …

Abstract Let n> 1 n>1 be a positive integer. Let RR be a henselian local ring with residue
field kk of nn th level sn (k) s_n(k). We give some upper and lower bounds for the nn th …