Related papers: On p-adic haromonic Maass functions

In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important role in the construction by Kohnen and…

Let $g \in S_{k}(\Gamma_{0}(N))$ be a normalized newform and $f$ be a harmonic Maass form that is good for $g$. The holomorphic part of $f$ is called a mock modular form and denoted by $f^{+}$. For odd prime $p$, K. Bringmann, P. Guerzhoy,…

We investigate a new family of locally harmonic Maass forms which correspond to periods of modular forms. They transform like negative weight modular forms and are harmonic apart from jump singularities along infinite geodesics. Our main…

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 note we extend integral weight harmonic Maass forms to functions defined on the upper and lower half-planes using the method of Poincar\'e series. This relates to Rademacher's "expansion of zero" principle, which was recently…

The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the…

We establish existence theorems for the image of the normalized character map of the $p$-adic Heisenberg algebra $S$ taking values in the algebra of Serre $p$-adic modular forms $M_p$. In particular, we describe the construction of an…

We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$-theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we…

This note points out that for any odd prime $p$, Zagier's weight $3/2$ mock Eisenstein series can be completed to a $p$-adic modular form in a way that bears some resemblance to its completion to a harmonic Maass form.

In this paper, we use regularized theta liftings to construct weak Maass forms weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proof of some of recent results of Duke, Toth and Imamoglu on cycle…

We come back to the construction of p-adic L-functions attached to cusp forms of even weight k in the spirit of G. Stevens, R. Pollack [7] and M. Greenberg [3] with a new unified presentation including the non-ordinary case. This…

The space of polyharmonic Maass forms was introduced by Lagarias-Rhoades, recently. They constructed its basis from the Taylor coefficients of the real analytic Eisenstein series. In this paper, we introduce polyharmonic weak Maass forms,…

Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on…

This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These…

Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms…

In this preprint we prove that any finite slope modular form fits into a p-adic family of modular forms which is indexed by the weight. Here, the term p-adic family means that p-adic congruences between weights entail certain p-adic…

Let $p$ be a prime. We discuss $p$-adic properties of various arithmetical functions related to the coefficients of modular form and generating functions. Modular forms are considered as a tool of solving arithmetical problems. Examples of…

We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a…

In this paper, we give a new geometric definition of nearly overconvergent modular forms and $p$-adically interpolate the Gauss-Manin connection on this space. This can be seen as an ``overconvergent'' version of the unipotent circle action…

We resolve a question of Kac, and explain the automorphic properties of characters due to Kac-Wakimoto pertaining to sl(m|n)^ highest weight modules, for n \geq 1. We prove that the Kac-Wakimoto characters are essentially holomorphic parts…