Related papers: Computing Theta Functions with Julia
Motivation: Estimating model parameters from experimental observations is one of the key challenges in systems biology and can be computationally very expensive. While the Julia programming language was recently developed as a high-level…
Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia…
We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating…
The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an…
Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…
We present FractionalDiffEq.jl, a comprehensive solver suite for solving fractional differential equations, featuring high-performance numerical algorithms in the Julia programming language. FractionalDiffEq.jl is designed to be…
A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.
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…
Jacobi's $\theta$ function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of $\theta(z,\tau)$, for $z, \tau$ verifying certain conditions, with precision $P$ in $O(\mathcal{M}(P)…
We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the…
We completely characterize the conformal radii of Siegel disks in the family $$P_\theta(z)=e^{2\pi i\theta}z+z^2,$$ corresponding to {\bf computable} parameters $\theta$. As a consequence, we constructively produce quadratic polynomials…
We introduce and study the Hilbert space of $(L^2,\Gamma,\chi)$-likewise theta functions on $\mathbb{R}^d$ with respect to a given discrete subgroup $\Gamma$ of arbitrary rank and a character $\chi$ of $\Gamma$. A concrete description is…
Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for…
The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on…
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…
TypedMatrices.jl is a Julia package to organize test matrices. By default, the package comes with a number of built-in matrices and interfaces to help users select test cases based on their properties. The package is designed to be…
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we…
In this paper we mainly investigate the radial distribution of Julia set of derivatives of entire solutions of some complex linear differential equations. Under certain conditions, we find the lower bound of it which improve some recent…
Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…
It is shown that the Jacobi and Riemann identities of degree four for the multidimensional theta functions as well as the Weierstrass identities emerge as algebraic consequences of the fundamental multidimensional binary identities…