6 papers
Integral Bases and Invariant Vectors for Weil Representations
Shaul Zemel
We show that the Weil representation associated with any discriminant form admits a basis in which the action of the representation involves algebraic integers. The action of a gen…
Shintani Lifts of Nearly Holomorphic Modular Forms
Yingkun Li, Shaul Zemel
In this paper, we compute the Fourier expansion of the Shintani lift of nearly holomorphic modular forms. As an application, we deduce modularity properties of generating series of…
Seesaw Identities and Theta Contractions with Generalized Theta Functions, and Restrictions of Theta Lifts
Shaul Zemel
We prove a seesaw identity for theta functions with polynomials, and establish a formula for the corresponding theta contractions. We then use it to determine the restrictions of t…
Moments of Partitions and Derivatives of Higher Order
Shaul Zemel
We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.
The Structure of Integral Parabolic Subgroups of Orthogonal Groups
Shaul Zemel
We determine the detailed structure of parabolic subgroups of orthogonal groups over , and deduce the precise form of canonical boundary components in toroidal compacti…
Thomae's Derivative Formulae for Trigonal Curves
Victor Enolski, Yaacov Kopeliovich, Shaul Zemel
In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational…