相关论文: Action of Hecke operators on Siegel theta series I…

We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues.

We introduce an alternate set of generators for the Hecka algebra, and give an explicit formula for the action of these operators on Fourier coefficients. With this, we compute the eigenvalues of Hecke operators acting on average Siegel…

We evaluate the action of Hecke operators on Siegel Eisenstein series of degree 2, square-free level and arbitrary character, without using knowledge of their Fourier coefficients. From this we construct a basis of simultaneous eigenforms…

We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalise the space with respect to all the Hecke operators, computing the…

We derive explicit formulas for the action of the Hecke operator $T(p)$ on the genus theta series of a positive definite integral quadratic form and prove a theorem on the generation of spaces of Eisenstein series by genus theta series. We…

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 characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of…

It is known that average Siegel theta series lie in the space of Siegel Eisenstein series. Also, every lattice equipped with an even integral quadratic form lies in a maximal lattice. Here we consider average Siegel theta series of degree 2…

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.

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;…

Let $D$ in $Z/2[[x]]$ be $\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally…

Fix a prime number p and choose, once and for all, an embedding of the algebraic closure of Q into Qp. Let k and N be integers, and suppose N is not divisible by p. If f is a modular form of weight k, level N, and trivial character which is…

We construct many examples of level one Siegel modular forms in the kernel of theta operators mod $p$ by using theta series attached to positive definite quadratic forms.

We present a method to compute two Hecke operators acting on a space of algebraic modular forms simultaneously based on an idea of Eichler's. We show that in certain cases this method can be used to obtain the action of the full Hecke…

We construct a basis for the space of half-integral weight Siegel Eisenstein series of level 4N where N is odd and square-free. Then we restrict our attention to those Eisenstein series generated from elements of $\Gamma_0(4)$, commenting…

We determine a formula for the average values of L-series associated to eigenforms at complex values.

Siegel modular forms in the space of the mod $p$ kernel of the theta operator are constructed by the Eisenstein series in some odd-degree cases. Additionally, a similar result in the case of Hermitian modular forms is given.

We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended…

For each prime $p$, we determine the distribution of the $p^{th}$ Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As $p\to\infty$, this distribution tends to the Sato--Tate distribution.

We construct a new family of mod $p$ weight shifting differential operators on the Siegel threefold. In particular, we construct one operator which generalizes the classical theta cycle, whose weight shift allows for maps between…