相关论文: Height zeta functions of equivariant compactificat…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
In this paper, we give an introduction to the rationality of the equivariant Morse stratification, and state the author's results on zeta functions of prehomogeneous vector spaces.
We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of a Matsumoto zeta-function and a periodic Hurwitz zeta-function…
This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.
We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…
Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.
The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds \Gamma\backslash{\Bbb H}^d and…
The aim of this paper is to apply the work of Morris on Eisenstein series over global function fields to the study of the asymptotic behavior of the points of bounded height on a generalized flag variety defined as the quotient of a…
The original article expressed the special values of the zeta function of a variety over a finite field in terms of the $\hat{Z}$-cohomology of the variety. As the article was being completed, Lichtenbaum conjectured the existence of…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
The aim of this paper is twofold: on one hand we study the invariants of traces of quadratic forms over a finite field of characteristic two. On the other hand, we give results about the zeta functions of certain curves studied by van der…
The local zeta functions (also called Igusa's zeta functions) over p-adic fields are connected with the number of solutions of congruences and exponential sums mod p^{m}. These zeta functions are defined as integrals over open and compact…
One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $\zeta(s)$, Hurwitz zeta function $\zeta(s,a)$ and Dirichlet $L$-function $L(s,\chi)$ at $s=1$. Moreover, we…
We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's…
We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the…
The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in…
We compute explicitly Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of various $p$-adic analytic and adelic profinite groups of type $\mathsf{A}_2$. This has consequences for the…
We present a conjectured formula for the representation zeta function of the Heisenberg group over $\mathcal{O}[x]/(x^n)$ where $\mathcal{O}$ is the ring of integers of some number field. We confirm the conjecture for $n\leq 3$ and raise…
We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the…
We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that the topological zeta function is a topological invariant for…