Related papers: Borcherds lifts of harmonic Maass forms and modula…

The Kudla lift studied in this article is a classical version for Picard modular forms of the automorphic theta lift between $\text{GU}(2)$ and $\text{GU}(3)$. We construct an explicit $p$-adic analytic family of Picard modular forms…

Let K be an imaginary quadratic field with discriminant -D, and x the Dirichlet character corresponding to the extension K/Q. Let m=2n or 2n+1 with n a positive integer. Let f be a primitive form of weight 2k+1 and level D with Neben…

In this paper we study generalizations of quadratic form Poincar\'e series, which naturally occur as outputs of theta lifts. Integrating against them yields evaluations of higher Green's functions. For this we require a new regularized…

We investigate integrality and divisibility properties of Fourier coefficients of meromorphic modular forms of weight $2k$ associated to positive definite integral binary quadratic forms. For example, we show that if there are no…

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to…

We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions. As an application we give a very explicit description of…

We use Borcherds products to give a new construction of the weight $3$ paramodular nonlift eigenform $f_N$ for levels $N = 61, 73, 79$. We classify the congruences of $f_N$ to Gritsenko lifts. We provide techniques that compute eigenvalues…

We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. Knopp…

Modular and mock modular forms possess many striking $p$-adic properties, as studied by Bringmann, Guerzhoy, Kane, Kent, Ono, and others. Candelori developed a geometric theory of harmonic Maass forms arising from the de Rham cohomology of…

In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of our efforts to extend in the noncompact…

For $K$ an imaginary quadratic field with discriminant $-D_K$ and associated quadratic Galois character $\chi_K$, Kojima, Gritsenko and Krieg studied a Hermitian Maass lift of elliptic modular cusp forms of level $D_K$ and nebentypus…

We establish the existence of the symmetric power liftings of all holomorphic Hecke eigenforms.

Following Zagier, this work studies the rationality and divisibility of Fourier coefficients of meromorphic Hilbert modular forms associated with real quadratic fields, using theta lifts and weak Maass forms. We establish conditions where…

We consider a special theta lift $\theta(f)$ from cuspidal Siegel modular forms $f$ on $\mathrm{Sp}_4$ to "modular forms" $\theta(f)$ on $\mathrm{SO}(4,4)$. This lift can be considered an analogue of the Saito-Kurokawa lift, where now the…

In this paper we consider several problems in the theory of automorphic products and generalized Kac--Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic…

In this paper, we explicitly construct harmonic Maass forms that map to the weight one theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic…

In this article, we are interested in modular forms with non-vanishing central critical values and linear independence of Fourier coefficients of modular forms. The main ingredient is a generalization of a theorem due to VanderKam to…

We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature (n-1,1). We construct an arithmetic theta lift from harmonic Maass forms of weight 2-n to the arithmetic Chow group of…

We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$…

In this note we show that certain meromorphic orthogonal modular forms are magnetic, i.e.\ their Fourier coefficients satisfy special divisibility criteria. These meromorphic orthogonal modular forms are counterparts to the orthogonal cusp…