Related papers: Computing Gamma(p/q) with Beta function values
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…
Algorithms are presented for calculating the partition function of constrained beta-gamma systems in terms of the generating functions of the individual fields of the theory, the latter obtained as the Hilbert series of the arc space of the…
Let f be a G-function (in the sense of Siegel), and x be an algebraic number; assume that the value f(x) is a real number. As a special case of a more general result, we show that f(x) can be written as g(1), where g is a G-function with…
Eta quotients on $\Gamma_0(6)$ yield evaluations of sunrise integrals at 2, 3, 4 and 6 loops. At 2 and 3 loops, they provide modular parametrizations of inhomogeneous differential equations whose solutions are readily obtained by expanding…
We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators.…
We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears…
The two dimensional $CP^1$ model with $\theta$ term is simulated. We compute the topological charge distribution $P(Q)$ by employing the ``set method" and ``trial function method", which are effective in the calculations for very wide range…
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
The fundamental aim of this paper is to describe q-Analogue of p-adic log gamma functions with weight alpha and beta. Moreover, we give relationship between p-adic q-log gamma funtions with weight ({\alpha}, {\beta}) and q-extension of…
We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.
A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.
From the realization of $q-$oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szeg\H{o} polynomials as well as…
For a germ of a meromorphic function f=P/Q, we offer notions of the monodromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the…
Let $p,x$ be real numbers, and $s$ be a complex number, with $\Re(s)>1-r$, $p\geq 1$, and $x+1>0$. The zeta function $Z^{\bf\alpha}_p(s;x)$ is defined by $$ Z^{\bf\alpha}_p(s;x) =\frac{1}{\Gamma(s)}\int^\infty_0 \frac{e^{-xt}}…
We give a polynomial time algorithm for computing the Igusa local zeta function $Z(s,f)$ attached to a polynomial $f(x)\in \QTR{Bbb}{Z}[x]$, in one variable, with splitting field $\QTR{Bbb}{Q}$, and a prime number $p$. We also propose a new…
An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical…
A complete and improved calculation of phase space factors (PSF) for $2\nu\beta\beta$ and $0\nu\beta\beta$ decay is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and…
We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function $\beta$ defined by $\beta(p^a)=p^a-p^{a-1}+p^{a-2}-...+(-1)^a$ for every prime power $p^a$ ($a\ge 1$), and extended by multiplicativity. Certain open…
It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $\eta(z)$, $\eta(2z)$ and $\eta(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…