Related papers: False Theta Functions and the Verlinde formula

We quantize the $W$-algebra W(2,2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell--Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving…

We show that formulas differing from classical analogues of rational trace formulas for algebraic-geometric potentials occur in the theory of finite-gap integration of spectral equations. The new formulas contain transcendental modular…

Let $X$ be a variety over a finite field. Given an order $R$ in a semi-simple algebra over the rationals and a constructible \'etale sheaf $F$ of $R$-modules over $X$, one can consider a natural non-commutative $L$-function associated with…

We define cylindric generalisations of skew Macdonald functions when one of their parameters is set to zero. We define these functions as weighted sums over cylindric skew tableaux: fixing two integers n>2 and k>0 we shift an ordinary skew…

Let $f$ be a holomorphic modular form of prime level $p$ and trivial nebentypus. We show that there exists a computable $\delta>0$, such that $$ L\left(\tfrac{1}{2},\mathrm{Sym}^2 f\right)\ll p^{\tfrac{1}{2}-\delta}, $$ with the implied…

We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…

We construct theta liftings from half-integral weight weak Maass forms to even integral weight weak Maass forms by using regularized theta integral. Moreover it gives an extension of Niwa's theta liftings on harmonic weak Maass forms. And…

Let $p$ and $l$ be rational primes such that $l$ is odd and the order of $p$ modulo $l$ is even. For such primes $p$ and $l$, and for $e=l, 2l$, we consider the non-singular projective curves $aY^e = bX^e + cZ^e$ ($abc \neq 0$) defined over…

Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra…

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…

Let K be an abelian extension of a totally real number field k, K^+ its maximal real subfield and G=Gal(K/k). We have previously used twisted zeta-functions to define a meromorphic CG-valued function Phi_{K/k}(s) in a way similar to the use…

Subregular W-algebras are an interesting and increasingly important class of quantum hamiltonian reductions of affine vertex algebras. Here, we show that the $\mathfrak{sl}_{n+1}$ subregular W-algebra can be realised in terms of the…

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…

We compare the dimensions of the irreducible Sp(2g,K)-modules over a field K of characteristic p constructed by Gow with the dimensions of the irreducible Sp(2g,F_p)-modules that appear in the first approximation to representations of…

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric…