Related papers: The algebraic meaning of genus-zero
Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in…
We will generalize Osburn's work about a congruence for traces defined in terms of Hauptmodul associated to certain genus zero groups of higher levels.
We present what we call a "motivated proof" of the Andrews-Bressoud partition identities for even moduli. A "motivated proof" of the Rogers-Ramanujan identities was given by G. E. Andrews and R. J. Baxter, and this proof was generalized to…
We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
MOND theory has arisen as a promising alternative to dark matter in explaining the collection of discrepancies that constitute the so-called missing mass problem. The MOND paradigm is briefly reviewed. It is shown that MOND theory can be…
Based on a sequence of numerical computations, a conjecture is presented regarding the class of functions $H(x;a)=\exp(a)-(1+a/x)^x$, and the open problem of determining the values of $a$ for which the functions are completely monotonic…
We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of…
This paper explores goal-directed proof search in first-order multi-modal logic. The key issue is to design a proof system that respects the modularity and locality of assumptions of many modal logics. By forcing ambiguities to be…
The sign coherence phenomenon is an important feature of c-vectors in cluster algebras with principal coefficients. In this note, we consider a more general version of c-vectors defined for arbitrary cluster algebras of geometric type and…
We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory,…
We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…
Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the…
Recently, it is well known that the conjectural integral identity is of crucial importance in the motivic Donaldson-Thomas invariants theory for non-commutative Calabi-Yau threefolds. The purpose of this article is to consider different…
It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…
The genus of projective curves discretely separates decidedly different two variable algebraic relations. So, we can focus on the connected moduli M_g of genus g curves. Yet, modern applications require a data variable (function) on such…
For certain subgroups of $M_{24}$, we give vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of…
The widely accepted dark matter hypothesis offers a seductive solution to missing mass problems (galaxies, clusters of galaxies, gravitational collapse in structure formation,...). However the physical nature of the Dark Matter itself is…
No more salient issue exists in contemporary astrophysics and cosmology than that of the elusive "dark matter". For many years already Milgrom's paradigm of modified Newtonian dynamics (MOND) has provided an alternative way to interpret…
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the…