Zeta Polynomials and the Möbius Function

The Arakawa–kaneko Zeta Function and Poly-bernoulli Polynomials

The purpose of this paper is to introduce a generalization of the Arakawa–Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.

The zeta function, L-functions, and irreducible polynomials

= 1 1− q1−s , where we have convergence for all s with <(s) > 1. This automatically gives us analytic continuation of ζ to all of C. We note the following simple observations: 1. The Riemann hypothesis: All zeroes of ζ lie on the line <(s) = 1/2, simply because there are no zeroes! 2. ζ has poles at s = 1 + 2πin log q . 3. Locally around s = 1, ζ has the Laurent series expansion: 1 (s− 1) log q...

Relations Between Möbius and Coboundary Polynomials

It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of the dual matroid, define the coboundary polynomial of the matroid. In some cases, the answer is aff...

The Möbius Function of Separable and Decomposable

We give a recursive formula for the Möbius function of an interval [σ, π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1, 2, . . . , k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficie...

A weighted Möbius function