相关论文: Formes modulaires modulo $2$ : L'ordre de nilpoten…

Suppose that $\ell \geq 5$ is prime. For a positive integer $N$ with $4 \mid N$, previous works studied properties of half-integral weight modular forms on $\Gamma_0(N)$ which are supported on finitely many square classes modulo $\ell$, in…

We present an explicit set of matrices giving the action of the Hecke operators $T(p)$, $T_j(p^2)$ on Siegel modular forms.

We describe a novel method for bounding the dimension $d$ of the largest simple Hecke submodule of $S_2(\Gamma_0(N);\mathbb{Q})$ from below. Such bounds are of interest because of their relevance to the structure of $J_0(N)$, for instance.…

Let $\ell \geq 5$ be a prime and let $N$ be a square-free integer prime to $\ell$. For each prime $p$ dividing $N$, let $a_p$ be either $1$ or $-1$. We give sufficient criteria for the existence of a newform $f$ of weight 2 for…

Let $\mathbf{A}$ be a finite nilpotent algebra in a congruence modular variety with finitely many fundamental operations. If $\mathbf{A}$ is of prime power order, then it is known that there is a polynomial $p$ such that for every $n \in…

In \cite{Shimura}, Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm's bounds give…

We let $f$ be a half-integral weight modular form of weight $\kappa>4$ on $\Gamma_0(4)$ that is an eigenfunction of all Hecke operators $T_n$, so that $T_nf = \Lambda_f(n)n^{\frac{\kappa-1}{2}}f$. Let $\|f\|$ denote the Petersson norm of…

For all $k \ge 2$, we show that there exists a group $G$ and a non-free stably free $\mathbb{Z} G$-module of rank $k$. We use this to show that, for all $k \ge 2$, there exist homotopically distinct finite $2$-complexes with fundamental…

Let $p$ be a rational prime and $q$ a power of $p$. Let $\wp$ be a monic irreducible polynomial of degree $d$ in $\mathbf{F}_q[t]$. In this paper, we define an analogue of the Hodge-Tate map which is suitable for the study of Drinfeld…

The modular properties of the simple vertex operator superalgebra associated to the affine Kac-Moody superalgebra $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$ at level $-\frac{5}{4}$ are investigated. After classifying the…

Let $G$ be a group and write $\mbox{Perm}(G)$ for its symmetric group. Define $\mbox{Hol}(G)$ to be the holomorph of $G$, regarded as a subgroup of $\mbox{Perm}(G)$, and let $\mbox{NHol}(G)$ denote its normalizer. The quotient $T(G) =…

I begin with a simple modular form motivated proof of the following: Let $C_{n}$ in $Z/2[[t]]$ be defined by $C_{n+4} = C_{n+3} + (t^{4}+t^{3}+t^{2}+t)C_{n} + t^{n}(t^{2}+t)$, with initial values $0$, $1$, $t$ and $t^{2}$ for $C_{0}$,…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

For a prime $p,$ let $\mathbb{F}_q$ be a finite extension of $\mathbb{F}_p.$ The restriction of an irreducible mod $p$ representation of $\text{GL}_2(\mathbb{F}_q)$ to its subgroup $\text{GL}_2(\mathbb{F}_p)$ can be seen as a tensor product…

We describe a computational approach to the verification of Maeda's conjecture for the Hecke operator T2 on the space of cusp forms of level one. We provide experimental evidence for all weights less than 12000, as well as some applications…

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra $\mathcal{H}_C(G,I(1))$, where G is the unramified unitary group U(2,1)(E/F) in…

Given a Hilbert cuspidal newform $g$ we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted $L$-series of $g$ by fundamental discriminants. The family is parametrized…

Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…

Let m>=1 be an arbitrary fixed integer and let N_m(x) count the number of odd integers u<=x such that the order of 2 modulo u is not divisible by m. In case m is prime estimates for N_m(x) were given by H. Mueller that were subsequently…

In this paper we prove that if the polar decomposition of a symbol $f$ is truncated above, i.e., $f(re^{i\theta} )=\sum_{k=-\infty}^Ne^{ik\theta} f_k (r)$ where the $f_k$'s are radial functions, and if the associated Toeplitz operator $T_f$…