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This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…
We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by…
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
In a recent paper with Sahi and Stokman, we introduced quasi-polynomial generalizations of Macdonald polynomials for arbitrary root systems via a new class of representations of the double affine Hecke algebra. These objects depend on a…
Kanade explored the construction of modular companions to $q$-series identities, using the asymptotics of Nahm sums, and Mizuno [Ramanujan J.\ {\bf 66} (2025), Paper No.\ 62, 31] recently obtained a generalization of Kanade's asymptotic…
Assuming that the string inspired, universal sum rules for soft supersymmetry-breaking terms, which have been recently found both in a wide class of four-dimensional superstrings and in supersymmertic gauge-Yukawa unified gauge models, are…
The radiative electroweak symmetry breaking, the b-\tau Yukawa and gauge couplings unification in the MSSM and its SU(5) extensions are studied in detail. In the framework of the two-loop renormalization group equations both low- and…
In recent years, the generalized sum-of-divisor functions of MacMahon have been unified into the algebraic framework of $q$-multiple zeta values. In particular, these results link partition theory, quasimodular forms, $q$-multiple zeta…
We study the representation theory of the type B Schur algebra $\mathcal{L}^n(m)$ with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of $q,Q$, this algebra is semi-simple and Morita equivalent to the…
We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…
In this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations among these series and propose an explicit conjectural…
We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…
We provide a $q$-analogue of Euler's formula for $\zeta(2k)$ for $k\in\mathbb{Z}^+$. Our main results are stated in Theorems 3.1 and 3.2 below. The result generalizes a recent result of Z.W. Sun who obtained $q$-analogues of…
We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.
We find a $q$-analog of the following symmetrical identity involving binomial coefficients $\binom{n}{m}$ and Eulerian numbers $A_{n,m}$, due to Chung, Graham and Knuth [{\it J. Comb.}, {\bf 1} (2010), 29--38]: {equation*} \sum_{k\geq…
We construct a family of $q$-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $\mathbb{Q}$-valued solution of the extended double shuffle equations. These…
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.
Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…
A multi-dimensional bilateral $q$-series extending the $q$-Selberg integral is studied using concepts of truncation, regularization and connection formulae. Following Aomoto's method, which involves regarding the $q$-series as a solution of…