238 research outputs found
Zeta functions of adjacency algebras of association schemes of prime order or rank two
For a module L which has only finitely many submodules with a given finite index we define the zeta function of L to be a formal Dirichlet series zeta(L) (s) = Sigma(n >= 1) a(n)n(-s) where a(n) is the number of submodules of L with index n. For a commutative ring R and an association scheme (X, S) we denote the adjacency algebra of (X, S) over R by RS. In this article we aim to compute zeta(ZS)(s), where ZS is viewed as a regular ZS-module, under the assumption that vertical bar X vertical bar is a prime or vertical bar S vertical bar = 2.ArticleHOKKAIDO MATHEMATICAL JOURNAL. 45(1):75-91 (2016)journal articl
Upper bounds on cyclotomic numbers
In this article, we give upper bounds for cyclotomic numbers of order e over
a finite field with q elements, where e is a divisor of q-1. In particular, we
show that under certain assumptions, cyclotomic numbers are at most
, and the cyclotomic number (0,0) is at most
, where k=(q-1)/e. These results are obtained by
using a known formula for the determinant of a matrix whose entries are
binomial coefficients.Comment: 11 pages, minor revisio
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