15 citations · 104 across the 38 of their papers we have counts for
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Modularity of special 0-cycles on toroidal compactifications of Shimura Varieties
Jan Hendrik Bruinier, Eugenia Rosu, Shaul Zemel
We consider the generating series of appropriately completed 0-dimensional special cycles on a toroidal compactification of an orthogonal or unitary Shimura variety with values in…
Hermitian Jacobi Forms Having Modules as their Index and Vector-Valued Jacobi Forms
Shaul Zemel
We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued…
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…
Jacobi Forms of Indefinite Lattice Index
Shaul Zemel
We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of th…
Special Cycles on Toroidal Compactifications of Orthogonal Shimura Varieties
Jan Hendrik Bruinier, Shaul Zemel
We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define…
The Origin of the Beauregard--Suryanarayan Product on Pythagorean Triples
Shaul Zemel
We show how the multiplicative structure on Pythagorean triples defined by Beauregard--Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem…
Shimura's Vector-Valued Modular Forms, Weight Changing Operators, and Laplacians
Shaul Zemel
We investigate the various types of weight raising and weight lowering operators on quasi-modular forms, or equivalently on Shimura's vector-valued modular forms involving symmetri…
Normalizers of Congruence Groups in and Automorphisms of Lattices
Shaul Zemel
We determine the normalizer in of several families of congruence subgroups of . In addition, we show how these tools can be used to evaluat…
Shimura Lifts of Weakly Holomorphic Modular Forms
Yingkun Li, Shaul Zemel
We show how to realize the Shimura lift of arbitrary level and character using the vector-valued theta lifts of Borcherds. Using the regularization of Borcherds' lift we extend the…
Regularized Pairings of Meromorphic Modular Forms and Theta Lifts
Shaul Zemel
We show that the meromorphic modular forms recently considered by Bringmann and Kane can be obtained as images of regularized theta lifts of Poincaré series under weight raising op…
Weight Changing Operators for Automorphic Forms on Grassmannians and Differential Properties of Certain Theta Lifts
Shaul Zemel
We define weight changing operators for automorphic forms on Grassmannians, i.e., on orthogonal groups, and investigate their basic properties. We then evaluate their action on the…
On Quasi-Modular Forms, Almost Holomorphic Modular Forms, and the Vector-Valued Modular Forms of Shimura
Shaul Zemel
We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power re…
A Gross--Kohnen--Zagier Type Theorem for Higher-Codimensional Heegner Cycles
Shaul Zemel
We prove that Heegner cycles of codimension m+1 inside Kuga-Sato type varieties of dimension 2m+1 are coefficients of modular forms of weight 3/2+m in the appropriate quotient grou…
A -adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices
Shaul Zemel
Suppose that is an even lattice with dual and level . Then the group , which is the unique non-trivial double cover of , admi…