Related papers: A characterization of the modular units
We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…
Recently, D. Choi obtained a description of the coefficients of the infinite product expansions of meromorphic modular forms over $\Gamma_0(N)$. Using this result, we provide some bounds on these infinite product coefficients for…
We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide a table of…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
We give an introduction to the concept of Kan extensions, and study its relation with the notions of coend and adjoint functors. We state and prove in detail a well known formula to compute Kan extensions by using coends: a certain colimit…
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of discriminant $-d$ evaluated at the modular $j$-function.…
A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations…
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
We give an explicit formula for dimensions of spaces of rational-weight modular forms whose multiplier systems are induced by eta-quotients of fractional exponents. As the first application, we give series expressions of Fourier…
We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…
In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.
We provide a module-theoretic interpretation of the expansion formula given by Huang (2022), which defines a map on perfect matchings to compute the expansion of quantum cluster variables in quantum cluster algebras arising from unpunctured…
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tanx, several expressions for log coshx and an identity for {\pi}2, from a series expansion of tan x, which gives the…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…