5 citations · 17 across the 21 of their papers we have counts for
21 papers
Schwarz maps for modular curves
Yaacov Kopeliovich, Camilo Sanabria Malagón
We solve a classical problem posed by F. Klein and studied by A. Hurwitz concerning the construction of linear ordinary differential equations associated with modular transformatio…
-Adic Functions for Cyclic Mumford Curve
Yaacov Kopeliovich
We express the branch points cross ratio of cyclic Mumford curves as quotients of -adic theta functions evaluated at the p-adic period matrix
The Fundamental Group of a Compact Riemann Surface via Branched Covers
Meirav Amram, Michael Chitayat, Yaacov Kopeliovich
Let be a compact Riemann surface of genus and let . We derive the classical presentation of (i.e the one given by generators $a_1,b_1, \dots, a_g,b…
Algebraic solution of the Jacobi inverse problem and explicit addition laws
Yaacov Kopeliovich
We formulate a solution to the Algebraic version of the Inverse Jacobi problem. Using this solution we produce explicit addition laws on any algebraic curve generalizing the law su…
Portfolio Optimization with Feedback Strategies Based on Artificial Neural Networks
Yaacov Kopeliovich, Michael Pokojovy
With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfol…
On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility
Yaacov Kopeliovich, Michael Pokojovy, Julia Bernatska
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e.,…
The fundamental group of compact Riemann surface
Yaacov Kopeliovich
We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle…
Igusa's map on modular forms vanishing on the hyperelliptic locus
J Bernatska, Y Kopeliovich
We extend Igusa's map to modular forms which vanish on the hyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishing derivatives of such modular forms are co…
Optimal control problems for stochastic processes with absorbing regime
yaacov Kopeliovich
In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial…
P-adic generalizations of hyper-elliptic functions
Yaacov Kopeliovich
We express the branch points cross ratio of Hyper-elliptic Mumford curves as quotients of p adic theta functions evaluated at the p adic period matrix
Solution of Mumford's second problem
Julia Bernatska, Yaacov Kopeliovich
A complete solution of Mumford's second problem about representation of theta derivatives with rational characteristics in terms of theta constants with rational characteristics is…
Addition via reduction algorithm on trigonal curves
Julia Bernatska, Yaacov Kopeliovich
In this paper we propose a direct and explicit realization of addition of divisors by means of an iterative reduction algorithm. Each iteration of the algorithm is the reduction of…
Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials
Julia Bernatska, Yaacov Kopeliovich
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbi…
The addition on Jacobian varieties from a geometric viewpoint
Yaacov Kopeliovich, Tony Shaska
We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebr…
Thomae's Derivative Formulae for Trigonal Curves
Victor Enolski, Yaacov Kopeliovich, Shaul Zemel
In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational…
Thomae formula for Abelian covers of
Yaacov Kopeliovich, Shaul Zemel
Abelian covers of , with fixed Galois group , are classified, as a first step, by a discrete set of parameters. Any such cover , of genus say, carri…
On Spaces Associated with Invariant Divisors on Galois Covers of Riemann Surfaces and Their Applications
Yaacov Kopeliovich, Shaul Zemel
Let be a Galois cover of Riemann surfaces, with Galois group . In this paper we analyze the -invariant divisors on , and their associated spaces of meromorphic…
General cyclic covers and their Thomae formula
Yaacov Kopeliovich
Let be a general cyclic cover of ramified at points, we define a class of non positive divisors on of degree supported in the pre i…
On theta functions of order four
Yaacov Kopeliovich, Christian Pauly, Olivier Serman
We prove that the fourth powers of theta functions with even characteristics form a basis of the space of even theta functions of order four on a principally polarized Abelian vari…
Modular equations of order and Theta functions
Yaacov Kopeliovich
An algorithm to obtain equations between theta functions with integral characteristics evaluated at and for is presented.
Theta constants identities for Jacobians of cyclic 3-sheeted covers of the sphere and representations of the symmetric group
Yaacov Kopeliovich
We find identities between theta constants with rational characteristics evaluated at period matrix of a cyclic 3 sheeted cover of the sphere with branch points $λ_1...λ_…