Related papers: Efficient computation of non-archimedean theta fun…
In this paper, we will prove the rationality of the Artin-Mazur zeta functions of some non-Archimedean dynamical systems.
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
An algorithm to compute Dirichlet $L$-functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the characters under consideration span a dyadic window.
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
The goal of this paper is to describe a theoretical construction of an infinite collection of non-classical Schottky groups. We first show that there are infinitely many non-classical noded Schottky groups on the boundary of Schottky space,…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
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 algebraic structure of iterated integrals has been encoded by Chen. Formally, it identifies with the shuffle and Lie calculus of Lyndon, Ree and Sch\"utzenberger. It is mostly incorporated in the modern theory of free Lie algebras.…
In this paper we consider an analogue of the zeta function for not necessarily prehomogeneous representations of GL(2) and compute some of the poles.
Motivated by rigorous development in the theory of digamma functions, we have first derived some new identities for the digamma function, and then computed the values of digamma function for the fractional orders using these identities…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over…
In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and…
Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear…
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…
A simple and efficient formula is proposed for varying Abelian integrals (including their periods) under variation of the generators of the classical Schottky group representing a Riemann surface.
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
This article concerned with the issue of solving a nonlinear equation with the help of iterative method where no any derivative evaluation is required per iteration. Therefore, this work contributes to a new class of optimal eighth-order…