Related papers: Negative index Jacobi forms and quantum modular fo…
Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and…
This paper is devoted to studying difference indices of quasi-regular difference algebraic systems. We give the definition of difference indices through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved.…
Let $\omega_\varphi^k(f,\delta)_{w,L_q}$ be the Ditzian-Totik modulus with weight $w$, $M^k$ be the cone of $k$-monotone functions on $(-1,1)$, i.e., those functions whose $k$th divided differences are nonnegative for all selections of…
We consider a general class of Fourier coefficients for an automorphic form on a finite cover of a reductive adelic group ${\bf G}(\mathbb{A}_{\mathbb{K}})$, associated to the data of a `Whittaker pair'. We describe a quasi-order on Fourier…
We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime $\ell$. Among the applications of this we show that there are $\gg \sqrt{X}/\log \log…
A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the lowest non-vanishing derivatives of theta functions with…
We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…
We explain how to use a certain new "Jacobi identity" for vertex operator algebras, announced in a previous paper (math.QA/9909178), to interpret and generalize recent work of S. Bloch's relating values of the Riemann zeta function at…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact…
We construct a tower of arithmetic generators of the bigraded polynomial ring J_{*,*}^{w, O}(D_n) of weak Jacobi modular forms invariant with respect to the full orthogonal group O(D_n) of the root lattice D_n for 2\le n\le 8. This tower…
We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a…
In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke…
We study the properties and asymptotics of the Jacobi matrices associated with equilibrium measures of the weakly equilibrium Cantor sets. These family of Cantor sets were defined and different aspects of orthogonal polynomials on them were…
This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…
There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q-brackets are quasimodular forms. We extend these families so that the corresponding q-brackets are quasimodular for a…
In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power series identities for some powers of $\triangle(q)$, where…
In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these coefficients to the algebraicity of the coefficients of certain canonical meromorphic…
In this paper we consider a semigroup of completely positive maps $\tau=(\tau_t,t \ge 0)$ with a faithful normal invariant state $\phi$ on a type-$II_1$ factor $\cla_0$ and propose an index theory. We :achieve this via a more general…
We show the modular properties of the multiple 'elliptic' gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's…