相关论文: Certain Siegel Cusp Forms with Level are Determine…

Motivated by weighted partition of $n$ that vanish if and only if $n$ is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes in the sense that the $n$-th Fourier coefficient vanishes…

The purpose of this paper is to prove that a primitive Hilbert cusp form $\mathbf{g}$ is uniquely determined by the central values of the Rankin-Selberg $L$-functions $L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})$, where $\mathbf{f}$ runs…

We prove that all mod $p^m$ singular forms of level $N$, degree $n+r$, and $p$-rank $r$ with $n\ge r$ are congruent mod $p^m$ to linear combinations of theta series of degree $r$ attached to quadratic forms of some level. Moreover, we prove…

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…

The theta series of the two unimodular even positive definite lattices of rank 16 are known to be linearly dependent in degree at most 3 and linearly independent in degree 4. In this paper we consider the next case of the 24 Niemeier…

In this paper, we calculate the Fourier coefficients of the paramodular twist of a Siegel modular form of paramodular level $N$ by a nontrivial quadratic Dirichlet character mod $p$ for $p$ a prime not dividing $N$. As an application, these…

Nondegenerate forms N of degree d on a unital nonassociative algebra A over a ring R which permit composition, i.e., satisfy N(1)=1 and N(xy)=N(x)N(y) for all x,y in A, are studied. These forms were first classified by Schafer over fields…

We extend the usual notion of Petersson inner product on the space of cuspidal Jacobi forms to include non-cuspidal forms as well. This is done by examining carefully the relation between certain "growth-killing" invariant differential…

We give coefficient formulas for antisymmetric vector-valued cusp forms with rational Fourier coefficients for the Weil representation associated to a finite quadratic module. The forms we construct always span all cusp forms in weight at…

We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show…

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants $D$ such that…

A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a…

Let $f$ be a primitive Maass cusp form for a congruence subgroup $\Gamma_0(D) \subset $ SL($2,\mathbb{Z}$) and $\lambda_f(n)$ its $n$-th Fourier coefficient. In this paper it is shown that with knowledge of only finitely many $\lambda_f(n)$…

We give a summary of results for dimensions of spaces of cuspidal Siegel modular forms of degree 2. These results together with a list of dimensions of the irreducible representations of the finite groups GSp(4,Fp) are then used to produce…

We establish Ramanujan-style congruences modulo certain primes $\ell$ between an Eisenstein series of weight $k$, prime level $p$ and a cuspidal newform in the $\varepsilon$-eigenspace of the Atkin-Lehner operator inside the space of cusp…

For positive integers $g$ and $N$, let $\mathcal{F}_N$ be the field of meromorphic Siegel modular functions of genus $g$ and level $N$ whose Fourier coefficients belong to the $N$th cyclotomic field. We present explicit generators of…

Let $F$ be an $L^2$-normalized Siegel cusp form for $\mathrm{Sp}_4(\mathbb{Z})$ of weight $k$ that is a Hecke eigenform and not a Saito--Kurokawa lift. Assuming the Generalized Riemann Hypothesis, we prove that its Fourier coefficients…

In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant…

We provide a power-saving bound for certain smoothed shifted convolution sums for Fourier coefficients of Siegel cusp forms. This result is the first nontrivial estimate for a shifted convolution sum with two cusp forms on a group of higher…

Let $f$ be a half-integral weight cusp form of level $4N$ for odd and squarefree $N$ and let $a(n)$ denote its $n^{\rm th}$ normalized Fourier coefficient. Assuming that all the coefficients $a(n)$ are real, we study the sign of $a(n)$ when…