Let G be a finite transitive group on a set , let , and let be the stabilizer of the point in G. In this paper, we are interested in the proportion that is, the proportion of elements of lying in a suborbit of cardinality at most 2. We show that, if…
An explicit formula forthe mean value of is known, where runs over all odd primitive Dirichlet characters of prime conductors p. Bounds on the relative class number of the cyclotomic field follow. Lately, the authors obtained that the mean value of …
For a given Beurling–Carleson subset E of the unit circle which has positive Lebesgue measure, we give explicit formulas for measurable functions supported on E such that their Cauchy transforms have smooth extensions from to . The existence of such …
We investigate quantum lens spaces, , introduced by Brzeziński and Szymański as graph -algebras. We give a new description of as graph -algebras amending an error in the original paper by Brzeziński and Szymański. Furthermore, for , we give a number-t…
Residual torsion-free nilpotence has proved to be an important property for knot groups with applications to bi-orderability and ribbon concordance. Mayland proposed a strategy to show that a two-bridge knot group has a commutator subgroup which is a u…
We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by a choice of left-invariant divergence operator gives rise to a Ricci curvature tensor, and we study the corresponding Einstein equ…
We describe the small-time heat kernel asymptotics of real powers , of a non-negative self-adjoint generalized Laplacian acting on the sections of a Hermitian vector bundle over a closed oriented manifold M. First, we treat separately the asymptotic…
Let be a finite Galois-algebra extension of a number field F, with group G. Suppose that is weakly ramified and that the square root of the inverse different is defined. (This latter condition holds if, for example, is odd.) Erez has conjectured t…
An affine variety with an action of a semisimple group G is called “small” if every nontrivial G-orbit in X is isomorphic to the orbit of a highest weight vector. Such a variety X carries a canonical action of the multiplicative group commuting with t…
We investigate the pluriclosed flow on Oeljeklaus–Toma manifolds. We parameterize left-invariant pluriclosed metrics on Oeljeklaus–Toma manifolds, and we classify the ones which lift to an algebraic soliton of the pluriclosed flow on the universal cove…