We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.

In this article we prove finite generation of the cohomology of quotients of a PBW algebra A by relating it to the cohomology of quotients of a quantum symmetric algebra S which is isomorphic to the associated graded algebra of A. The proof uses a spectral sequence argument and a finite generation lemma adapted from Friedlander and Suslin.

In this note we consider a question of Ono, concerning which spaces of classical modular forms can be generated by sums of η-quotients. We give some new examples of spaces of modular forms which can be generated as sums of η-quotients, and show that we can write all modular forms of level Γ0(N) as rational functions of η-products.

This paper has two purposes. We determine the automorphism groups of the 2-transitive, bilinear dual hyperovals over F2 of type D[k], which were constructed in [6] by the author. Secondly, we characterize 2-transitive quotients of the Huybrechts dual hyperoval, compute their automorphism groups and give estimates on the number of such quotients.

A finite simplicial graph Γ determines a right-angled Artin group GΓ, with generators corresponding to the vertices of Γ, and with a relation vw = wv for each pair of adjacent vertices. We compute the lower central series quotients, the Chen quotients, and the (first) resonance variety of GΓ, directly from the graph Γ.

We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.

Let a and m be integers such that (a, m) = 1. Let qa = aφ(m)−1 m . We call qa the Euler Quotient of m with base a. This is called the Fermat Quotient when m is a prime. We consider some properties of the matrix of Euler Quotients reduced modulo m and show that these quotients are uniformly distributed modulo m.

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

This paper gives a partial desingularisation construction for hyperkähler quotients and a criterion for the surjectivity of an analogue of the Kirwan map to the cohomology of hyperkähler quotients. This criterion is applied to some linear actions on hyperkähler vector spaces.