相关论文: Periodicity of traces of Hecke operators modulo pr…
We prove multiplicity one for vector valued holomorphic Siegel modular forms of weights greater or equal to 3 and the full Siegel modular group and give a trace formula for the action of the Hecke operators T(p) in the regular cases.
We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…
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…
A Hecke action on the space of periods of cusp forms, which is compatible with that on the space of cusp forms, was first computed using continued fraction and an explicit algebraic formula of Hecke operators acting on the space of period…
Matrix representations of Hecke operators on classical holomorphical cusp forms and corresponding period polynomials are well known. In this article we define Hecke operators on period functions and show that they correspond to the Hecke…
We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.
In this mostly expository note, we prove explicit formulas for the traces of Hecke operators on spaces of cusp forms fixed by Atkin-Lehner involutions, which are suitable for efficient implementation. In addition, we correct a couple of…
In this paper, we study the Drinfeld cusp forms for $\Gamma_1(T)$ and $\Gamma(T)$ using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the…
We provide formulas for traces of p-th Hecke operators in level 1 in terms of values of finite field 2F1-hypergeometric functions, extending previous work of the author to all odd primes p, instead of only those p=1 (mod 12). We first give…
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…
Let S_{w+2} be the vector space of cusp forms of weight w+2 on the full modular group, and let S_{w+2}^* denote its dual space. Periods of cusp forms can be regarded as elements of S_{w+2}^*. The Eichler-Shimura isomorphism theorem asserts…
Let $(P_d)$ be any prime of $\mathbb{F}_q[t]$ of degree $d$ and consider the space of Drinfeld cusp forms of level $P_d$, i.e. for the modular group $\Gamma_0(P_d)$. We provide a definition for oldforms and newforms of level $P_d$.…
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;…
In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus \mathrm{A}_1$,…
Matrix representations of Hecke operators on classical holomorphical cusp forms and the corresponding period polynomials are well known. In this article we derive representations of Hecke operators for vector valued period functions for the…
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite…
We calculate the effect of simple Hecke operators on u-expansions of higher rank Drinfeld modular forms, the eigenvalue for the Drinfeld discriminant function $\Delta_t$ and show that a certain natural class of Hecke operators is completely…
Inspired by Borcherds' questions, Guerzhoy constructed a new type of Hecke operators $\mathcal{T}(p)$, called the multiplicative Hecke operators, which acts on the space of meromorphic modular forms on the full modular group ${\rm SL}(\Z)$.…
We calculate the action of some Hecke operators on spaces of modular forms spanned by the Siegel theta-series of certain genera of strongly modular lattices closely related to the Leech lattice. Their eigenforms provide explicit examples of…
We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, yielding congruences for their coefficients modulo powers of primes. As an application we derive systematic congruences for several higher-order…