Related papers: On quantum modular forms of non-zero weights

In this note we consider infinite series similar to the "strange" function $F(q)$ of Kontsevich studied by Zagier, Bryson-Ono-Pitman-Rhoades, Bringmann-Folsom-Rhoades, Rolen-Schneider, and others in connection to quantum modular forms. We…

We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent…

The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs…

For any square-free integer $N$ such that the "moonshine group" $\Gamma_0(N)^+$ has genus zero, the Monstrous Moonshine Conjectures relate the Hauptmoduli of $\Gamma_0(N)^+$ to certain McKay-Thompson series associated to the representation…

Let $U_q$ be the quantum group corresponding to a complex simple Lie algebra $\mathfrak g$ with root system $R$. Assume the quantum parameter $q\in \C$ is a root of unity. In this paper we study the extensions between simple modules in the…

Let $E$ be a level 1, vector valued Eisenstein series of half-integral weight, normalized so that the coefficients are all in $\mathbb{Z}$. We show that there is a level one vector valued cusp form $f$ with the same weight as $E$ and with…

Let $f\colon M \to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$-manifold $M$ without boundary, $n\ge 2$. We show that, for $k \in \{0,\ldots, n\}$, the induced homomorphism $f^* \colon…

We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…

We study continuity and regularity of convex extensions of functions from a compact set $C$ to its convex hull $K$. We show that if $C$ contains the relative boundary of $K$, and $f$ is a continuous convex function on $C$, then $f$ extends…

Radiation-filled Friedmann-Robertson-Walker universes are quantized according to the Arnowitt-Deser-Misner formalism in the conformal-time gauge. Unlike previous treatments of this problem, here both closed and open models are studied, only…

Motivated by the 1920's seminal work of Major MacMahon, Amdeberhan--Andrews--Tauraso recently introduced an infinite family of $q$-series \[ \mathcal{U}_{t}(a;q):= \sum_{1\le n_1<n_2<\cdots<n_t}…

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a…

Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

Let $k =\mathbb{F}_q$ be the finite field of $q$ elements and $E$ an elliptic curve over $k$. Let $F = k(E)$ be the function field over $E$ and let $\mathcal{O} = k[E]$ be the ring of integers. We fix the place at $\infty$ of $F$ and let…

By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms. We establish,…

We study the bimodule structure of the quantum function algebra at roots of 1 and prove that it admits an increasing filtration with factors isomorphic to the tensor products of the dual of Weyl modules $V_\lambda^* \otimes V_{- \omega_0…

We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which…

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the…

We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…