We study modular differential equations for the basic weak Jacobi forms in one abelian variable with applications to elliptic genus of Calabi--Yau varieties. show that any $CY_3$ satisfies a equation degree respect heat operator. For $K3$ surface or $CY_5$ is $3$. prove general $CY_4$ its $5$. give examples two operator similar Kaneko--Zagier variable. find type $2$ $3$ second, third and fourth...

We show that all self-adjoint extensions of semi-bounded Sturm--Liouville operators with general limit-circle endpoint(s) can be obtained via an additive singular form bounded perturbation rank equal to the deficiency indices, say $d\in\{1,2\}$. This characterization generalizes well-known analog for regular endpoints. Explicitly, every extension minimal operator written as \begin{align*} \bold...

We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective) flat connection on this family coming from a heat operator. They also possess modular properties similar to the classical ones.

We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate’s theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin’s U-operator applied to a Jacobi form to be nonzero modulo a prime.

The bc-system of higher rank introduced recently is examined further. Its correlation functions are expressed through certain non-Abelian theta-functions and it is shown how quasideterminants arise. The associated U(1)-current is described geometrically and some local computations for the operator product expansions are made.

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

We define a theta operator on p-adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which p is inert. We study its effect on Fourier-Jacobi expansions and prove that it extends holomorphically beyond the μ-ordinary locus, when applied to scalar-valued forms.