Related papers: Jacobi Theta-functions and Discrete Fourier Transf…

We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This…

We find identities between theta constants with rational characteristics evaluated at period matrix of $R,$ a cyclic 3 sheeted cover of the sphere with $3k$ branch points $\lambda_1...\lambda_{3k}.$ These identities follow from Thomae…

Liu established an addition formula for the Jacobian theta function by using the theory of elliptic functions. From this addition formula he obtained the Ramanujan cubic theta function identity, Winquist's identity, a theta function…

We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions $n<7$ over algebraically closed fields of…

We prove that formal Fourier Jacobi expansions of degree 2 are Siegel modular forms. As a corollary, we deduce modularity of the generating function of special cycles of codimension 2, which were defined by Kudla. A second application is…

In a private communication, K. Ono conjectured that any mock theta function of weight 1/2 or 3/2 can be congruent modulo a prime $p$ to a weakly holomorphic modular form for just a few values of $p$. In this paper we describe when such a…

In this paper, we give some extensions for Ramanujan's circular summation formula with the mixed products of two Jacobi's theta functions. As some applications, we also obtain many interesting identities of Jacobi's theta functions.

In this note we consider functions with Moebius-periodic rational coefficients. These functions under some conditions take algebraic values and can be recovered by theta functions and the Dedekind eta function. Special cases are the…

In this study, we introduce a new class of quaternions associated with the well-known modified third-order Jacobsthal numbers. There are many studies about the quaternions with special integer sequences and their generalizations. All of…

This paper presents a preliminary version of the deformation theory of expressions of elements of algebras. The notion of *-functions is given. Several important problems appear in simplified forms, and these give an intuitive bird's-eye of…

We classify the optimal mock Jacobi forms of weight one with rational coefficients. The space they span is thirty-four-dimensional, and admits a distinguished basis parameterized by genus zero groups of isometries of the hyperbolic plane.…

The purpose of this paper is to investigate the distribution of zeros of entire functions which can be represented as the Fourier transforms of certain admissible kernels. The principal results bring to light the intimate connection between…

Using twisted Fock spaces, we formulate and study two twisted versions of the n-point correlation functions of Bloch-Okounkov, and then identify them with q-expectation values of certain functions on the set of (odd) strict partitions. We…

We give a transformation formula for the ``2nd order'' mock theta function which was recently proposed in connection with the quantum invariant for the Seifert manifold.

We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…

One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…

We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters $(1/4,1/4,1)$ and theta constants. By using this analogy and twice formulas of theta constants, we obtain a transformation formula for this…

It is shown that every weak Jacobi form of weight zero and index one on a congruence subgroup of the full Jacobi group can be decomposed into $N=4$ superconformal characters. Additionally, a simple expression for the mock modular form…

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher $Q^2$. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a…

We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric…