Related papers: On Kuznetsov-Bykovskii's formula of counting prime…

Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effective version of this theorem was first established by Lagarias…

We use a (pre)-Kuznetsov type formula to prove a density result for the Borel-type congruence subgroup of GLn. This has some arithmetic applications to optimal lifting and counting considered earlier by A. Kamber and H. Lavner for $GL_3$.

This note complements a recent paper of Chatzakos, Harcos and Kaneko \cite{CHK}. We use a Dirichlet style Prime Geodesic Theorem to improve the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…

Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of…

We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a…

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

Reduction formulas for sums of products of hypergeometric functions can be traced back to Euler. This topic has an intimate connection to summation and transformation formulas, contiguous relations and algebraic properties of the…

For $\Gamma$ a cofinite Kleinian group acting on $\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\Gamma \backslash \mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics)…

We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalisation of Vorono\"i's algorithm for computing perfect forms,…

We give a new proof of the best presently known error term in the prime geodesic theorem for compact Riemann surfaces, without the assumption of excluding a set of finite logarithmic measure. Stronger implications of the Gallagher-Koyama…

We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the positivity of certain structure constants for the associated Kazhdan--Lusztig basis. We also…

The Kazakov-Migdal model, if considered as a functional of external fields, can be always represented as an expansion over characters of $GL$ group. The integration over "matter fields" can be interpreted as going over the {\it model} (the…

Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the…

For an algebraic number field K with 3-class group \(Cl_3(K)\) of type (3,3), the structure of the 3-class groups \(Cl_3(N_i)\) of the four unramified cyclic cubic extension fields \(N_i\), \(1\le i\le 4\), of K is calculated with the aid…

We devise calculus rules for the Kurdyka-\L{}ojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local…

We use $K$-theory to prove an isomorphism theorem for a large class of generalised Bunce-Deddens algebras constructed by Kribs and Solel from a directed graph $E$ and a sequence $\omega$ of positive integers. In particular, we compute the…

This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…

In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…