Related papers: Modular equations of order $p$ and Theta functions
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with…
The simplest nontrivial tau functions of the Toda lattice and the $\tN$-component Toda lattice are compared in their applications to multimatrix integrals.
We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…
An analytic representation with Theta functions on a torus, for systems with variables in Z(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is…
In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work math.AG/0310085 and prove that for any n>1 the map sending an abelian variety to the set of Gauss…
We construct the theta function solution to the initial value problem for the generalized periodic discrete Toda equation.
An elementary method is given for estimates of the norms of the Toeplitz operators, determined by rational inner functions
We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.
We give a new method for constructing vector-valued modular forms from singular scalar-valued ones. As an application we prove the identity between two remarkable spaces of vector-valued modular forms which seem to be unrelated at a first…
This paper discuss a new class of functional equations by using both Poisson summation formula and Jacobi type theta a function. The class of Riemann type functional equations are derived from self-reciprocal probability density functions.…
We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains of type $I$. In our framework, each theta relation is controlled by combinatorial properties of a pair $(T,P)$ of…
In this article we obtain, using an expression of the digamma function $\psi(x)$ due to Mikolas, integral representations of the zeta function of odd arguments $\zeta(2p+1)$ for any positive value of $p$. The integrand consists of the…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We propose an algorithm to find a solution to an integro-differential equation of the DGLAP type for all the orders in the running coupling $\alpha$ with splitting functions given at a fixed order in $\alpha.$ Complex analysis is…
We discuss an arithmetic approach to some congruence properties of Siegel theta series of even positive definite unimodular quadratic forms.
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…