Related papers: A modularity criterion for Klein forms, with an ap…

We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational…

In this text, we develop the theory of vectorial modular forms with values in Tate algebras introduced by the first author, in a very special case (dimension two, for a very particular representation of {\Gamma} := GL 2 (Fq[$theta$])).…

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…

Jacobi forms can be considered as vector valued modular forms, and Jacobi forms of critical weight correspond to vector valued modular forms of weight $\frac12$. Since the only modular forms of weight $\frac12$ on congruence subgroups of…

In this article we give a criterion for a mod $\ell$ eigenvalue system attached to a mod $\ell$ Katz cuspform to arise from lower level or weight. Namely, we prove the following: the eigenvalue system associated to a ring homomorphism…

Modular symbols for the congruence subgroup $\Gamma_0(\mathfrak{n})$ of $GL_{2}(\mathbf{F}_q[T])$ have been defined by Teitelbaum. They have a presentation given by a finite number of generators and relations, in a formalism similar to…

In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\infty$ and $0$. As an application, we give explicit…

By adapting the work of Kudla and Millson we obtain a lifting of cuspidal cohomology classes for the symmetric space associated to GO(V) for an indefinite rational quadratic space V of even dimension to holomorphic Siegel modular forms on…

We say that a normalized modular form is of CM type modulo $\ell$ by an imaginary quadratic field $K$ if its Fourier coefficients $a_p$ are congruent to $0$ modulo a prime $\mathcal L\mid \ell$ for every prime $p$ that is inert in $K$. In…

We give sharp point-wise bounds in the weight-aspect on fourth moments of modular forms on arithmetic hyperbolic surfaces associated to Eichler orders. Therefore we strengthen a result of Xia and extend it to co-compact lattices. We realize…

Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be the congruence subgroup of level n consisting of matrices…

A semiclassical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the…

The main result of this paper is a characterization of the abelian varieties $B/K$ defined over Galois number fields with the property that the zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for…

Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the…

Recently, Allen et al. developed the Explicit Hypergeometric Modularity Method (EHMM) that establishes the modularity of a large class of hypergeometric Galois representations in dimensions two and three. Motivated by this framework, we…

We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite…

In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case $A = \mathbb{F}_q[T]$. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and…

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $\Gamma_0(4)$ with Kohnen's plus condition and…

Let $F$ be a totally real number field and $\mathfrak{o}$ the ring of integers of $F$. We study theta functions which are Hilbert modular forms of half-integral weight for the Hilbert modular group $\mathrm{SL}_2(\mathfrak{o})$. We obtain…

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…