Related papers: A class of non-holomorphic modular forms III: real…

We obtain a generalisation of the Quantum Unique Ergodicity for holomorphic cusp forms on $\mathrm{SL}_2(\mathbb{Z}) \backslash \mathbb{H}$ in the weight aspect. We show that correlations of masses coming from off-diagonal terms dissipate…

We define a subspace of the space of holomorphic modular forms of weight $k+1/2$ and level $4M$ where $M$ is odd and square-free. We show that this subspace is isomorphic under the Shimura-Niwa correspondence to the space of newforms of…

We construct Hecke operators acting on Maass waveforms of integer non-zero weight and transforming according to a non-trivial multiplier system on the modular group. Using these Hecke operators we obtain multiplicativity relations for the…

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…

A cusp form $f(z)$ of weight $k$ for $\SL_{2}(\Z)$ is determined uniquely by its first $\ell := \dim S_{k}$ Fourier coefficients. We derive an explicit bound on the $n$th coefficient of $f$ in terms of its first $\ell$ coefficients. We use…

In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit…

We characterize the irreducible, admissible, spherical representations of GSp(4,F) (where F is a p-adic field) that occur in certain CAP representations in terms of relations satisfied by their spherical vector in a special Bessel model.…

Notable results on the special values of $L$-functions of Siegel modular forms were obtained by J. Sturm in the case when the degree $n$ is even and the weight $k$ is an integer. In this paper we extend this method to half-integer weights…

To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields…

We study the vector space V_k^m(\lambda) of shifted polyharmonic Maass forms of weight k \in 2Z, depth m \geq 0, and shift \lambda \in C. This space is composed of real-analytic modular forms of weight k for PSL(2,Z) with moderate growth at…

Let $M_k^\sharp(4)$ be the space of weakly holomorphic modular forms of weight $k$ and level $4$ that are holomorphic away from the cusp at $\infty$. We define a canonical basis for this space and show that for almost all of the basis…

In this note, we describe several new examples of holomorphic modular forms on the group SU(2,1). These forms are distinguished by having weight $\frac{1}{3}$. We also describe a method for determining the levels at which one should expect…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

In this paper, we investigate the "angular changes" behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts…

We study congruences between cuspidal modular forms and Eisenstein series at levels which are square-free integers and for equal even weights. This generalizes our previous results from Naskr\k{e}cki [17] for prime levels and provides…

We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry-Ganguly-Kowalski-Michel and Kowalski-Ricotta in the context of half-integral weight…

Using holomorphic projection, we work out a parametrization for all relations of products (resp. Rankin-Cohen brackets) of weight $\tfrac 32$ mock modular forms with holomorphic shadow and weight $\tfrac 12$ modular forms in the spirit of…

We classify ``arithmetic convection equations'' on modular curves, and describe their space of solutions. Certain of these solutions involve the Fourier expansions of the Eisenstein modular forms of weight 4 and 6, while others involve the…

In this paper, we consider modular forms for finite index subgroups of the modular group whose Fourier coefficients are algebraic. It is well-known that the Fourier coefficients of any holomorphic modular form for a congruence subgroup…

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…