Related papers: Jacobi's Inversion Problem for Genus Two Hyperelli…

The elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds is computed. This is used to search for possible mirror pairs of such models. An important aspect of this work is that there is no restriction to theories for…

We show that the topological elliptic genus from the cobordism ring of SU-manifolds to topological Jacobi forms lifts to connective topological Jacobi forms, and that this lift is surjective in homotopy.

We investigate some aspects of N=2 twisted theories with matter hypermultiplets in the fundamental representation of the gauge group. A consistent formulation of these theories on a general four-manifold requires turning on a particular…

We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for $SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are new, not…

Let $k$ be a subfield of $\mathbb{C}$ which contains all $2$-power roots of unity, and let $K = k(\alpha_{1}, \alpha_{2}, ... , \alpha_{2g + 1})$, where the $\alpha_{i}$'s are independent and transcendental over $k$, and $g$ is a positive…

In this work we obtain algebraicity results on special $L$-values attached to Siegel-Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a…

From any given Frobenius manifold one may construct a so-called dual structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying…

We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian…

Genus 2 curves have been an object of much mathematical interest since eighteenth century and continued interest to date. They have become an important tool in many algorithms in cryptographic applications, such as factoring large numbers,…

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…

Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…

We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to…

A recursion relation of hyperelliptic psi functions of genus two, which was derived by D.G. Cantor (J. reine angew. Math. 447 (1994) 91-145), is studied. As Cantor's approach is algebraic, another derivation is presented as a natural…

We prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems. Using the (A,C) inversion formula to invert one of the known C-type elliptic beta integrals, we obtain a new elliptic…

We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also…

This article shows explicit relation between fractional expressions of Schottky-Klein type for hyperelliptic $\sigma$-functions and a product of differences of the algebraic coordinates on each stratum of natural stratification in a…

In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic…

This is an extended (factor 2.5) version of arXiv:math/0601371 and arXiv:0808.3486. We present new results in the theory of the classical $\theta$-functions of Jacobi: series expansions and defining ordinary differential equations (\odes).…

This paper investigates a class of special Berndt-type integral calculations where the integrand contains only hyperbolic cosine functions. The research approach proceeds as follows: Firstly, through contour integration methods, we…

We compute the class of arithmetic genus two Teichmueller curves in the Picard group of pseudo-Hilbert modular surfaces, distinguished according to their torsion order and spin invariant. As an application, we compute the number of genus…