Related papers: Equidistribution of cusp forms in the level aspect

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the…

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…

Let f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infinity. This generalizes known results in the case that q is…

For each prime $\ell$, let $|\cdot|_\ell$ be an extension to $\bar \Q$ of the usual $\ell$-adic absolute value on $\Q$. Suppose $g(z) = \sum_{n=0}^\infty c(n)q^n \in M_{k+\half}(N)$ is an eigenform whose Fourier coefficients are algebraic…

Let $Y_1$ be a compact arithmetic hyperbolic surface associated to a maximal quaternion order, let $Y_q$ be a cover associated to an Eichler suborder of prime level $q$, and let $\iota_q$ be embedding of $Y_q$ as the Hecke correspondence…

We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over…

It was shown in previous works that the measure associated to holomorphic newforms of weight $k$ and level $q$ will tend weakly to the Haar measure on modular curve of level 1, as $qk\rightarrow \infty$. In this paper we proved that this…

In 2000 Iwaniec, Luo, and Sarnak proved for certain families of $L$-functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infinity the one-level density…

In this paper we give a new proof of the Quantum Unique Ergodicity conjecture for holomorphic integral weight modular forms on the upper half plane. The proof requires only partial results towards the Ramanujan conjecture and the shifted…

We refine known dimension formulas for spaces of cusp forms of squarefree level, determining the dimension of subspaces generated by newforms both with prescribed global root numbers and with prescribed local signs of Atkin-Lehner…

This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised…

Let $f=\sum_{n=1}^{\infty}a(n)q^{n}\in S_{k+1/2}(N,\chi_{0})$ be a non-zero cuspidal Hecke eigenform of weight $k+\frac{1}{2}$ and the trivial nebentypus $\chi_{0}$ where the Fourier coefficients $a(n)$ are real. Bruinier and Kohnen…

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $GSp_4/\mathbb{Q}$ in various aspects. A main tool is Arthur's invariant trace formula. While Shin and Shin-Templier used Euler-Poincar\'e functions at…

We show, for levels of the form $N = p^a q^b N'$ with $N'$ squarefree, that in weights $k \geq 4$ every cusp form $f \in \mathcal{S}_k(N)$ is a linear combination of products of certain Eisenstein series of lower weight. In weight $k=2$ we…

We show that if a modular cuspidal eigenform $f$ of weight $2k$ is $2$-adically close to an elliptic curve $E/\mathbb{Q}$, which has a cyclic rational $4$-isogeny, then $n$-th Fourier coefficient of $f$ is non-zero in the short interval…

This paper studies the Fourier expansion of Hecke-Maass eigenforms for $GL(2, \mathbb Q)$ of arbitrary weight, level, and character at various cusps. Translating well known results in the theory of adelic automorphic representations into…

We study the behavior of zeros and mass of holomorphic Hecke cusp forms on $SL_2(\mathbb Z) \backslash \mathbb H$ at small scales. In particular, we examine the distribution of the zeros within hyperbolic balls whose radii shrink…

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that…

In this paper we apply results from the theory of congruences of modular forms (control of reducible primes, level-lowering), the modularity of elliptic curves and Q-curves, and a couple of Frey curves of Fermat-Goldbach type, to show the…

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…