Related papers: On Denert's statistic
We show that Mahler's classification of real numbers $\zeta$ with respect to the growth of the sequence $(w_{n}(\zeta))_{n\geq 1}$ is equivalently induced by certain natural assumptions on the decay of the sequence…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
We prove analytic and combinatorial identities reminiscent of Schur's classical partition theorem. Specifically, we show that certain families of overpartitions whose parts satisfy gap conditions are equinumerous with partitions whose parts…
We find an explicit general formula for the iterated local monodromy of singularities of the Hadamard product of functions with integrable singularities. The formula implies the invariance by Hadamard product of the class of functions with…
Chaudhry and Qadir obtained new identities for the gamma function by using a distributional representation for it. Here we obtain new identities for the Riemann zeta function and its family by using that representation for them. This also…
We determine the special values at positive integers of the spectral zeta function associated with the combinatorial Laplacian on the regular tree. These values admit explicit formulas in terms of certain polynomials, which we show to be…
We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…
Euler discovered a formula for expressing the value of the Riemann zeta function for all even positive integer arguments. A closed-form expression for the Riemann zeta function for all odd integer arguments, based on the values of the…
We obtain two-variable Hecke-Rogers identities for three universal mock theta functions. This implies that many of Ramanujan's mock theta functions, including all the third order functions, have a Hecke-Rogers-type double sum…
We prove a regularized determinant formula for the zeta functions of certain 3-dimensional Riemannian foliated dynamical systems, in terms of the infinitesimal operator induced by the flow acting on the reduced leafwise cohomologies. It is…
In the present paper, we show that the motivic Hilbert zeta function for a curve singularity yields the generating functions for Euler numbers of punctual Hilbert schemes when any punctual Hilbert scheme admits an affine cell decomposition.…
We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach…
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series…
Let (G,H) be one of the equal rank reductive dual pairs (Mp_{2n},O_{2n+1}) or (U_n,U_n) over a non-archimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain…
The aim of this paper is to define some new number-theoretic functions including necklaces polynomials and the numbers of special words such as Lyndon words. By using Dirichlet convolution formula with well-known number-theoretic functions,…
By a similar idea for the construction of Milnor's gamma functions, we introduce "higher depth determinants" of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a generalization of the determinant…
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…
The eigenvalue probability density function of the Gaussian unitary ensemble permits a $q$-extension related to the discrete $q$-Hermite weight and corresponding $q$-orthogonal polynomials. A combinatorial counting method is used to specify…
We recast the local factors of the Hasse-Weil zeta function at infinity in terms of the Cuntz-Pimsner algebras. The nature of such factors is an open problem studied by Deninger and Serre.
In this paper, by introducing a new operation in the vector space of Laurent series, the author derived explicit series for the values of $\zeta$-funtion at positive integers, where $\zeta$ denotes the Riemann zeta function. The values of…