相关论文: q-Bernoulli Numbers and Zeros of q-Sine Function

We present a numerical study of Riemann's formula for the oscillating part of the density of the primes and their powers. The formula is comprised of an infinite series of oscillatory terms, one for each zero of the zeta function on the…

The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some…

This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a…

In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving…

In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from…

This paper provides some expansions of Riemann xi function, $\xi$, as a series of Bessel K functions.

In this paper, we investigate a specific class of $q$-polynomial sequences that serve as a $q$-analogue of the classical Appell sequences. This framework offers an elegant approach to revisiting classical results by Carlitz and, more…

The Bernoulli numbers b_0,b_1,b_2,.... of the second kind are defined by \sum_{n=0}^\infty b_nt^n=\frac{t}{\log(1+t)}. In this paper, we give an explicit formula for the sum \sum_{j_1+j_2+...+j_N=n,…

The derivative of the Riemann zeta function was computed numerically on several large sets of zeros at large heights. Comparisons to known and conjectured asymptotics are presented.

By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space…

We derive an equation that is analogous to a well-known symmetric function identity: $\sum_{i=0}^n(-1)^ie_ih_{n-i}=0$. Here the elementary symmetric function $e_i$ is the Frobenius characteristic of the representation of $\mathcal{S}_i$ on…

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we evaluate those double series. Our main results can be regarded as a certain…

In this paper, we focus on a q-analogue of the Riemann zeta function at positive integers, which can be written for s\in\N^* by \zeta_q(s)=\sum_{k\geq 1}q^k\sum_{d|k}d^{s-1}. We give a new lower bound for the dimension of the vector space…

We prove some identities, which involve the non-trivial zeros of the Riemann zeta function. From them we derive some convergent asymptotic expansions related to the work by Cram\'er, and also new representations for some arithmetical…

We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\psi_q(x)$, and the $q$-series.…

In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.

In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the…

By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…