Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0708.3306

Carlitz q-Bernoulli numbers and q-Stirling numbers

Taekyun Kim
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.

Explore related subjects

math.NT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Taekyun Kim. 2007-08-24. Carlitz q-Bernoulli numbers and q-Stirling numbers. https://arxiv.org/abs/0708.3306

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Database of Continued Fractions of Polynomial Type

We describe a database of 1925 continued fractions with polynomial coefficients, of which more than 1600 are new, both for interesting constants and for transcendental functions, and provide the database inside the \TeX\ source of the paper. Look in particular at the section ``Table of Contents''.

math.NT↗
arXiv2026

On properness of moduli stacks of $D^{\times}$-shtukas over ramified legs

Given a maximal order $\mathcal{D}$ of a central division algebra $D$ over a global function field $F$, we prove an explicit necessary and sufficient condition for moduli stacks of $\mathcal{D}^\times$-shtukas to be proper over a finite field (modulo a suitable central action) in terms of the local invariants of $D$ and bounds. Our result extends E. Lau's criterion (Duke Math. J. 140 (2007)) for properness of the leg morphism (or characteristic morphism) away from the ramification locus of $D$ to allow legs at ramified places. We also establish non-emptiness of Newton and Kottwitz-Rapoport strata for moduli stacks of $\mathcal{B}^\times$-shtukas, where $\mathcal{B}$ is a maximal order of a central simple algebra over $F$.

math.NT↗
arXiv2026

Cuspidal distinction via intertwining periods

Local intertwining periods have so far been used to reduce distinction of a general irreducible representation to distinction of cuspidal ones, for which other tools -- type theory, local and global trace formulae -- take over. The main contribution of this paper is to prove that they can be used to decide distinction of cuspidal representations themselves. We develop this approach with three well-studied examples for which the ambient group is an inner form of $\mathrm{GL}_n$ over a $p$-adic field, namely linear models, their non-split twisted version, and the quaternionic symplectic model. As consequences, we obtain proofs valid in arbitrary residual characteristic of the cuspidal case of the epsilon dichotomy conjecture of Prasad and Takloo-Bighash and of Prasad's conjecture on quaternionic symplectic models. The proof in the quaternionic symplectic model case, although going through intertwining periods, uses the simplest ones, namely closed intertwining periods, and is disappointingly short and elementary.

math.NT↗