Related papers: Shintani Lifts of Nearly Holomorphic Modular Forms

We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all…

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

We study Fourier transforms of regular holonomic D-modules. In particular we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic D-modules will be given. Moreover we give a new…

We give some examples of isomorphisms of moduli of sheaves induced by Fourier-Mukai functor. As applications, we give another proof on deformation type of some moduli spaces of sheaves on abelian and K3 surfaces.

In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between…

We prove the boundedness of a general class of multipliers and Fourier multipliers, in particular of the Hilbert transform, on quasi-Banach modulation spaces. We also deduce boundedness for multiplications and convolutions for elements in…

We establish upper bounds for shifted moments of modular $L$-functions to a fixed modulus as well as quadratic twists of modular $L$-functions under the generalized Riemann hypothesis. Our results are then used to establish bounds for…

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

In this paper we use automorph class theory formalism to construct a lifting of similitudes of quadratic Z-modules of arbitrary ternary nondegenerate quadratic forms to morphisms between certain subrings of associated Clifford algebras. The…

This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…

In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.

Holomorphic modular bootstrap is an approach to classifying rational conformal field theories making use of the modular differential equations. In this paper we explore its flavored refinement. For a class of chiral algebras, we propose…

We describe a construction of preimages for the Shimura map on Hilbert modular forms, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted L-functions. Our construction is inspired…

In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $\xi$-operator. As a result, we show that their holomorphic parts have algebraic…

We study polynomial growth holomorphic functions and forms on complete gradient shrinking Ricci solitons. By relating to the spectral data of the $f$-Laplacian, we show that the dimension of the space of polynomial growth holomorphic…

The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.

There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a…

In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke…

We construct almost holomorphic and holomorphic modular forms by considering theta series for quadratic forms of signature $(n-1,1)$. We include homogeneous and spherical polynomials in the definition of the theta series (generalizing a…

We show that the base spaces of the semiuniversal unfoldings of some weighted homogeneous singularities can be identified with moduli spaces of $A_\infty$-structures on the trivial extension algebras of the endomorphism algebras of the…