Related papers: Sato Grassmannian and Degenerate Sigma Function

We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic…

In this paper, we give an algorithm to generate connection formulas of generalized hypergeometric functions ${}_p F_{p-1}$ for degenerated values of parameters. We also show that these connection formulas give a fast method for numerical…

In this paper we introduce a new family of the KP tau-functions. This family can be described by a deformation of the generalized Kontsevich matrix model. We prove that the simplest representative of this family describes a generating…

We study the non-minimal supersymmetric heterotically deformed $\mathcal{N}=(0,2)$ sigma model with the Grassmannian target space $\mathcal{G}_{M,N}$. To develop the appropriate superfield formalism, we begin with a simplified model with…

For elliptic curves over rationals, there are a well-known conjecture of Sato-Tate and a new computational guided murmuration phenomenon, for which the abelian Hasse-Weil zeta functions are used. In this paper, we show that both the…

Sato theory provides a correspondence between solutions to the KP hierarchy and points in an infinite dimensional Grassmannian. In this correspondence, flows generated infinitesimally by powers of the ``shift'' operator give time dependence…

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae…

In this paper, we give a generate function for the $\sigma_1$ function. Then we find some connections between the $\sigma_1$ function and the Ramanujan's tau function. We hope this connection will give some insights into the unsolved…

Here we review some recent developments in the theory of isomonodromic deformations on Riemann sphere and elliptic curve. For both cases we show how to derive Schlesinger transformations together with their action on tau-function, and…

This is the second paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated in mathematical physics. In the first article in this series we defined geometric families of these functions…

We study symmetries enjoyed by the polynomials enumerating non-degenerate flags in finite vector spaces, equipped with a non-degenerate alternating bilinear, hermitian or quadratic form. To this end we introduce Igusa-type rational…

This survey is devoted to the classical and modern problems related to the entire function ${\sigma({\bf u};\lambda)}$, defined by a family of nonsingular algebraic curves of genus $2$, where ${\bf u} = (u_1,u_3)$ and $\lambda = (\lambda_4,…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

In the last decades, the theory of digamma function has been developed with a high impact of interest by many authors. Here, we established some interesting results for digamma function, and also we have computed the values of digamma…

The generating functions of stationary descendent Gromov-Witten invariants of an elliptic curve are known to be Fourier expansions of quasimodular forms. When one restricts to the subspace of forms of a fixed weight $k$, there is an…

In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of…

The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…

We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten…

Current and upcoming experiments should improve the sensitivity to radiative lepton decays by an order of magnitude. This paper assumes that one of the tau --> (e, mu) gamma decays is observed, and explores the structure and consequences of…