Related papers: Transformation Formula of the "2nd" Order Mock The…
We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for…
We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion…
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…
This paper is devoted to the study of the $M$-Wright function ($M_{\alpha}(t)$) which is the inverse Laplace transform of the single-parameter Mittag-Leffler (ML) function ($E_{\alpha}(-s)$). Because $E_{\alpha}(-s)$ can be viewed as the…
We construct a deformation of the quantum algebra Fun(T^*G) associated with Lie group G to the case where G is replaced by a quantum group G_q which has a bicovariant calculus. The deformation easily allows for the inclusion of the current…
We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the…
We obtain formulas for the coefficients of positive and negative powers of a partial theta function.
The nilpotence order of the mod 2 Hecke operators. Let $\Delta=\sum_{m=0}^\infty q^{(2m+1)^2} \in F_2[[q]]$ be the reduction mod 2 of the $\Delta$ series. A modular form f modulo 2 of level 1 is a polynomial in $\Delta$. If p is an odd…
In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…
In this series we examine the calculation of the $2k$th moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper is concerned with the precise…
Inspired by the results of the Ising model within an imaginary external magnetic field, we introduce a transformation in quantum systems with a theta-vacuum term that amounts to a rescaling of z=cos(theta/2). Making use of this…
We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants…
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…
We show that the Fourier transform on the Jacobian of a curve interchanges "$\delta$ functions" at the curve and the theta divisor. The Torelli theorem is an immediate consequence.
We develop a $\kappa$-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order $\kappa$-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma…
In this paper, transformation formulas for the function \[ A_{1}\left(z,s:\chi\right)=\sum\limits_{n=1}^{\infty}\sum\limits_{m=1}^{\infty}\chi\left(n\right)\chi\left(m\right)\left(-1\right)^{m}n^{s-1}e^{2\pi imnz/k} \] are obtained. Sums…
An easy generalization of Beukers' integrals allows us to conjecture a double integral formula involving the zeta and the gamma functions. A special case of this formula is Sondow's double integral formula for Euler's constant gamma.
We give a representation of the classical Riemann $\zeta$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen…
Unary theta functions have played a significant role in the theory of holomorphic modular forms and modular $L$-functions. A partial theta functions is defined analogously, but the sum is over part of the integer lattice. Such sums fail to…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…