Character sums in finite fields
We improve the known upper bound of the dimension of an indecomposable unimodular lattice whose shadow has the third largest possible length, .
A power digraph modulo , denoted by , is a directed graph with as the set of vertices and as the edge set, where and are any positive integers. In this paper we find necessary and sufficient conditions on and such that the digraph has at least one isolated fixed point. We also establish necessary and sufficient conditions on and such that the digraph contains exactly two components. The primality of Fermat number is also discussed.
Consider the families of curves and where A is a nonzero rational. Let and denote their respective Jacobian varieties. The torsion points of and are well known. We show that for any nonzero rational A the torsion subgroup of is a 2-group, and for A ≠ 4a⁴,-1728,-1259712 this subgroup is equal to (for a excluded values of A, with the possible exception of A = -1728, this group has a point of order 4). This is a variant of the corresponding results for (A ≠ 4) and . We also almost...
In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus by subsets of . Here we consider new types of subgroups: let be a Kronecker set (a compact set on which every continuous function can be uniformly approximated by characters of ), and the group generated by . We prove (Theorem 1) that can be characterized by a subset of (instead of a subset of ). If is finite, Theorem 1 implies our earlier result...
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.