Related papers: One Level Density for Cubic Galois Number Fields

We study certain unitary CM fields whose Galois closure has Galois group $\operatorname{PSL}_2(\mathbb{F}_q) \times \mathbb{Z}/2\mathbb{Z}$. After investigating the CM types of these fields, we turn towards Colmez's conjectural formula on…

It is believed that, in the limit as the conductor tends to infinity, correlations between the zeros of elliptic curve $L$-functions averaged within families follow the distribution laws of the eigenvalues of random matrices drawn from the…

For $n\geq 4$ (even), the function $\varphi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk $\mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this paper, the class $\mathcal{S}^*_{n\mathcal{L}} =…

Based on Garner's discovery that topological categories are total categories enriched in a quantaloid, this paper presents a series of results related to initial and final density in categorical topology via (co)density in…

In this paper, we study moments of central values of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$ and one level density result for the low-lying zeros of sextic Hecke $L$-functions of $\mathbb{Q}(\omega)$. As a corollary, we deduce…

We obtain the $n$th centered moments of one level densities of a large orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q\sim Q$. We verify the Katz-Sarnak conjecture for these…

In this paper we introduce new densities on the set of primes of a number field. If $K/K_0$ is a Galois extension of number fields, we associate to any element $x \in {\rm Gal}_{K/K_0}$ a density $\delta_{K/K_0,x}$ on primes of $K$. In…

We compute all signatures of $PSL_2(\mathbb{F}_7)$, and $PSL_2(\mathbb{F}_{11})$ which classify all orientation preserving actions of the groups $PSL_2(\mathbb{F}_7)$, and $PSL_2(\mathbb{F}_{11})$ on compact, connected, orientable surfaces…

When ordered by discriminant, it is known that about 83% of quartic fields over Q have associated Galois group S_4, while the remaining 17% have Galois group D_4. We study these proportions over a general number field F. We find that…

The Katz-Sarnak philosophy states that statistics of zeros of $L$-function families near the central point as the conductors tend to infinity agree with those of eigenvalues of random matrix ensembles as the matrix size tends to infinity.…

We investigate the large weight (k --> oo) limiting statistics for the low lying zeros of a GL(4) and a GL(6) family of L-functions, {L(s,phi x f): f in H_k(1)} and {L(s,phi times sym^2 f): f in H_k(1)}; here phi is a fixed even Hecke-Maass…

In this paper, we evaluate explicitly certain quadratic Hecke Gauss sums of $\mathbb{Q}(\omega), \omega=\exp \left( \frac {2\pi i}{3}\right)$. As applications, we study the moments of central values of quadratic Hecke $L$-functions of…

Katz and Sarnak conjectured a correspondence between the $n$-level density statistics of zeros from families of $L$-functions with eigenvalues from random matrix ensembles. In many cases the sums of smooth test functions, whose Fourier…

A famous conjecture of Keating and Snaith asserts that central values of $L$-functions in a given family admit a log-normal distribution with a prescribed mean and variance depending on the symmetry type of the family. Based on a recent…

The Galois group of a family of cubic surfaces is the monodromy group of the 27 lines of its generic fibre. We describe a method to compute this group for linear systems of cubic surfaces using certified numerical computations. Applying…

This text answers a question raised by Joux and the second author about the computation of discrete logarithms in the multiplicative group of finite fields. Given a finite residue field $\bK$, one looks for a smoothness basis for $\bK^*$…

Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a…

For a totally real number field $F$ and its ad\`ele ring $\mathbb{A}_F$, let $\pi$ vary in the set of irreducible cuspidal automorphic representations of ${\rm PGL}_2(\mathbb{A}_F)$ corresponding to primitive Hilbert modular forms of a…

Let n be an odd number and F an imaginary quadratic field with odd discriminant. We show that there exists infinitely many cubic fields K such that the class number of K is divisible by n and the Galois closure of K contains F.

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite…