Related papers: Automorphic forms for some even unimodular lattice…

We prove that for a Hecke cuspform $f\in S_k(\Gamma_0(N),\chi)$ and a prime $l>\max\{k,6\}$ such that $l\nmid N$, there exists an infinite family $\{k_r\}_{r\geq 1}\subseteq\mathbb{Z}$ such that for each $k_r$, there is a cusp form…

We construct some families of automorphic forms on Grassmannians which have singularities along smaller sub Grassmannians, using Harvey and Moore's extension of the Howe (or theta) correspondence to modular forms with poles at cusps. Some…

Recently, Allen, Grove, Long, and Tu proposed an explicit Hypergeometric-Modularity method which gives a concrete link between certain hypergeometric objects and modular forms. The theory is exemplified by a collection of 199 weight 3…

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 Jacobi forms (both in the orthogonal and Hermitian…

We find two combinatorial identities on the theta series of the root lattices of the finite-dimensional simple Lie algebras of type $D_{4n}$ and the cosets in their integral duals, in terms of the well-known Essenstein series $E_4(z)$ and…

In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them. In most cases the…

We give an explicit dimension formula for paramodular forms of degree two of prime level with plus or minus sign of the Atkin--Lehner involution of weight $\det^k\operatorname{Sym}(j)$ with $k\geq 3$, as well as a dimension formula for…

We present a new flavor of TAF-type (co)homology theories, which are p-local of height two and based on the isometry group of the odd unimodular hermitian lattice of signature (1,1) over the Gaussian integers. Using a suitable family of…

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…

In this paper we outline the Hecke theory for Hermitian modular forms in the sense of Hel Braun for arbitrary class number of the attached imaginary-quadratic number field. The Hecke algebra turns out to be commutative. Its inert part has a…

We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein…

In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…

Let $A$ be a finite dimensional hereditary algebra over a field $k$ and $A^{(1)}$ the duplicated algebra of $A$. We first show that the global dimension of endomorphism ring of tilting modules of $A^{(1)}$ is at most 3. Then we investigate…

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the…

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in $\mathbb{Q}(\sqrt{-3})$ are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.

We derive an explicit formula for the Hecke eigenvalues of a Hilbert modular form which is a base-change lift of a classical newform to a totally real Galois number field. We show that for a totally real abelian number field $F$ the…

We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. invertible 3 x 3 matrix whose (3, 3) entry is 0). Among…

Let $E/L$ be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of $\mathrm{GL}(2,E)$ which contains a Hilbert modular form with $\Gamma_0$ level to an…

We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…

By adapting the work of Kudla and Millson we obtain a lifting of cuspidal cohomology classes for the symmetric space associated to GO(V) for an indefinite rational quadratic space V of even dimension to holomorphic Siegel modular forms on…