Topic
Dirichlet density
About: Dirichlet density is a research topic. Over the lifetime, 68 publications have been published within this topic receiving 651 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, it was shown that a pure, regular, totally odd, polarizable weakly compatible system of rational primes is potentially automorphic, and that such a system is irreducible under Katz's theory of rigid local systems.
Abstract: In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity assumption instead. For compatible systems coming from geometry, purity is often easier to check than irreducibility. We use Katz's theory of rigid local systems to construct many examples of motives to which our theorem applies. We also show that if $F$ is a CM or totally real field and if $\pi$ is a polarizable, regular algebraic, cuspidal automorphic representation of $GL_n(\A_F)$, then for a positive Dirichlet density set of rational primes $l$, the $l$-adic representations $r_{l,\imath}(\pi)$ associated to $\pi$ are irreducible.
46 citations
TL;DR: In this article, a prior distribution is constructed on the space of stepwise constant density functions, not necessarily of bounded support, for the purpose of nonparametric density estimation, where the sequence of heights is conditionally distributed a prior in a Dirichlet process on the integers, given a bidimensional mixing parameter.
Abstract: For the purpose of nonparametric density estimation, a prior distribution is constructed on the space of stepwise constant density functions, not necessarily of bounded support. In particular, the sequence of heights is conditionally distributed a priorias a Dirichlet process on the integers, given a bidimensional mixing parameter. Such a mixing parameter is composed of a bin width and a starting point which are, in turn, assigned an arbitrary marginal prior. Proper Bayesian estimates of the density are obtained. They are not histograms, but they share common features with the histogram and other kernel based estimators. They also incorporate prior information, like a prior guess for the density or bounds for its support, which may be particularly appealing for small sample situations, where usual density estimation methods are not satisfactory. The estimates are computable by simple numerical methods, as opposed to other nonparametric Bayesian density estimators proposed in the literature, which display ...
20 citations
TL;DR: A generalized Dirichlet model is introduced in this article, which extends the standard real type-2 Dirichlets density, and many properties of this new model are studied, which enhance the possibility of applications in different directions.
11 citations
TL;DR: In this paper, a simple proof of a standard zero-free region in the $t$-aspect for the Rankin-Selberg $L$-function for any unitary cuspidal automorphic representation is given.
Abstract: We give a simple proof of a standard zero-free region in the $t$-aspect for the Rankin--Selberg $L$-function $L(s,\pi \times \widetilde{\pi})$ for any unitary cuspidal automorphic representation $\pi$ of $\mathrm{GL}_n(\mathbb{A}_F)$ that is tempered at every nonarchimedean place outside a set of Dirichlet density zero.
10 citations
TL;DR: In this paper, it was shown that the Fermat equations do not admit non-trivial solutions for a set of exponents p with Dirichlet density 1/4 and 1/8, respectively.
9 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 2 |
| 2019 | 4 |
| 2018 | 2 |
| 2017 | 7 |
| 2016 | 10 |