Related papers: Volkov's Pentagon for the Modular Quantum Dilogari…
The aim of the research presented in this paper is to derive the systems of ordinary differential equations (ODEs) satisfied by modular forms of level six and to construct extensions of the differential field of the cubic theta functions,…
We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general level than earlier work of Hijikata-Pizer-Shemanske for…
We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists in the reformulation of the delay…
For each subset of primes in a totally real field above a rational prime $p$, there is the notion of partially classical Hilbert modular forms, where the empty set recovers the overconvergent forms and the full set of primes above $p$…
Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they have the same dimensions as in the…
We focus our attention, once again, on the Klein--Gordon and Dirac equations with a plane-wave field. We recall that for the first time a set of solutions of these equations was found by Volkov. The Volkov solutions are widely used in…
Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result - under certain mild restrictions on the level and character - to the case of weight 1/2 Hilbert…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and…
Using Littlewood's map, which decomposes a partition into its $r$-core and $r$-quotient, Han and Ji have shown that many well-known hook-length formulas admit modular analogues. In this paper we present a variant of the Han-Ji…
Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal…
We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
The inhomogeneous quantum groups $IGL_q(n)$ are obtained by means of a particular projection of $GL_q(n+1)$. The bicovariant differential calculus on $GL_q(n)$ is likewise projected into a consistent bicovariant calculus on $IGL_q(n)$.…
We obtain a condition describing when the quasimodular forms given by the Bloch-Okounkov theorem as $q$-brackets of certain functions on partitions are actually modular. This condition involves the kernel of an operator {\Delta}. We…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We analyze the structure of Feigin-Stoyanovsky's principal subspaces of affine Lie algebra from the jet algebra viewpoint. For type $A$ level one principal subspaces, we show that their shifted multi-graded Hilbert series can be expressed…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…