Related papers: A note on Gekeler's h-function

Hoffstein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms $f_1$ and $f_2$. The second two authors investigated certain special values of symmetrized sums of such functions, numbers…

Given modular forms $f$ and $g$ of weights $k$ and $\ell$, respectively, their Rankin-Cohen bracket $[f,g]^{(k, \ell)}_n$ corresponding to a nonnegative integer $n$ is a modular form of weight $k +\ell +2n$, and it is given as a linear…

In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

We study properties of recently introduced Wieferich primes for Drinfeld modules, as their relation with Fermat equations and finitess or non-finiteness of their number. We also introduce Mersenne numbers for Drinfeld modules, and study the…

We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…

We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to…

For an isotropic subgroup $H$ of a discriminant form $D$ there exists a lift from modular forms for the Weil representation of the discriminant form $H^\bot/H$ to modular forms for the Weil representation of $D$. We determine a set of…

The aim of this paper is to describe some partial advances in the solution of the following two problems. Find the maximal order of vanishing at infinity of a non-zero Drinfeld quasi-modular form of given weight. Determine differential…

This work is a survey of relations between Drinfeld modules and higher dimensional fields of positive characteristic. The main new result stated is the expression of vanishing orders of certain modular forms through partial zeta values.

We construct explicit Drinfel'd twists of Jordanian type for the generalized Cartan type K Lie algebras in characteristic 0 and obtain the corresponding quantizations, especially their integral forms. By making modular reductions including…

We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…

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…

A description is given of all primitive differential series mod p of order 1 which are eigenvectors of all the Hecke operators and which are differential Fourier expansions of differential modular forms of arbitrary order and given weight;…

We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…

We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three…

Let $k$ be a global function field with field of constants $\Fr$ and let $\infty$ be a fixed place of $k$. In his habilitation thesis \cite{boc2}, Gebhard B\"ockle attaches abelian Galois representations to characteristic $p$ valued cusp…

We study a class of meromorphic modular forms characterised by Fourier coefficients that satisfy certain divisibility properties. We present new candidates for these so-called magnetic modular forms, and we conjecture properties that these…

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…

We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose $q$-expansions satisfy \[ f_k(A, \tau) \colon = q^{-k}(1+a(1)q+a(2)q^2+...) + O(q),\] where $a(n)$ are…