相关论文: Multiplicative relations for Fourier coefficients …

We extend some recent work of D. McCarthy, proving relations among some Fourier coefficients of a degree 2 Siegel modular form $F$ with arbitrary level and character, provided there are some primes $q$ so that $F$ is an eigenform for the…

Given two Siegel eigenforms of different weights, we determine explicit sets of Hecke eigenvalues for the two forms that must be distinct. In degree two, and under some additional conditions, we determine explicit sets of Fourier…

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight g/2 and genus g. When g=4, the Fourier coefficient is approximated…

We compute the Fourier coefficients of all degree 2 Siegel-Eisenstein series of square-free level $N$ transforming with the trivial character. We then apply use these formulae to present some explicit examples of higher representation…

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 investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ of degree 2, weight $k$ and level $N$. First, assuming that $F$ is a Hecke eigenform that is not of…

We prove a formula of Petersson's type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficient. The method in this…

Although links between values of finite field hypergeometric functions and eigenvalues of elliptic modular forms are well known, we establish in this paper that there are also connections to eigenvalues of Siegel modular forms of higher…

We compute Hecke eigenform bases of spaces of level one, degree~three Siegel modular forms and 2-Euler factors of the eigenforms through weight 22. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known…

In this paper we treat the Fourier coefficients of Siegel Eisenstein series of level $p$ with trivial or quadratic character, for an odd prime $p$. The Euler $p$-factor of the Fourier coefficient is called the ramified Siegel series. First…

We extend Igusa's description of the relation between invariants of binary sextics and Siegel modular forms of degree two to a relation between covariants and vector-valued Siegel modular forms of degree two. We show how this relation can…

We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an…

In a recent work, we found formulas for the Fourier coefficients of automorphic forms of type $G_2$: holomorphic Siegel modular forms on $\mathrm{Sp}_6$ that are theta lifts from $G_2^c$, and cuspidal quaternionic modular forms on split…

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…

We prove new bounds for the Fourier coefficients of Jacobi forms using a method of Iwaniec. In view of the Fourier-Jacobi expansion of degree two Siegel modular forms, we can use these to obtain strong bounds on fundamental Fourier…

Let $f$ and $f'$ be genus $2$ cuspidal Siegel paramodular newforms. We prove that if their Hecke eigenvalues $a_p$ and $a_p'$ satisfy a non-trivial polynomial relation $P(a_p, a_p') = 0$ for a set of primes $p$ of positive density, then $f$…

In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from the signs of their Hecke eigenvalues. To establish our theorem, we obtain a result towards simultaneous sign changes of eigenvalues…

We prove that a Siegel cusp form of degree 2 for the full modular group is determined by its set of Fourier coefficients a(S) with 4 det(S) ranging over odd squarefree integers. As a key step to our result, we also prove that a classical…

Sturm obtained the bounds for the number of the first Fourier coefficients of elliptic modular form $f$ to determine vanishing of $f$ modulo a prime $p$. In this paper, we study analogues of Sturm's bound for Siegel modular forms of genus…

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by $\mathbb{Q}(\sqrt{-3})$ and the other by $\mathbb{Q}(\sqrt{-2})$. The values of the $p$-th Fourier coefficients of all the forms in…