相关论文: A variation of multiple $L$-values arising from th…

This is a survey of recent progress on understanding the value distribution of zeta and L-functions. The article is intended for the 2022 ICM.

We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating…

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a…

We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…

In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…

Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…

Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this article, we focus on the asymptotic behavior at the origin $(0,\dots, 0)$ and unveil the generating series of the asymptotic…

Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…

The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vign\'{e}ras multiple gamma functions by considering the classical limit of the multiple…

We study the algebra MD of generating function for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in Q arising from the…

The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is…

Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.

A spectral representation for regularly varying L\'evy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the $L^2$-case where the…

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbol{\alpha})$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbol{\alpha})$. Then we consider…

In this article, we develop two types of asymptotic formulas for harmonic series in terms of single non-trivial zeros of the Riemann zeta function on the critical line. The series is obtained by evaluating the complex magnitude of an…

The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin…

We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share…