Related papers: On the probabilities of local behaviors in abelian…

The article at hand contains exact asymptotic formulas for the distribution of conductors of abelian p-extensions of global function fields of characteristic p. These yield a new conjecture for the distribution of discriminants fueled by an…

In this paper we investigate higher moments attached to the Chebotarev Density Theorem. Our focus is on the impact that peculiar Galois group structures have on the limiting distribution. Precisely we consider in this paper the case of…

Let $E$ be a field satisfying the following conditions: (i) the $p$-component of the Brauer group Br$(E)$ is nontrivial whenever $p$ is a prime number for which $E$ is properly included in its maximal $p$-extension; (ii) the relative Brauer…

Let $V$ be a projective limit, with respect to the renormalized norm mappings, of the groups of principal units corresponding to a strictly increasing sequence of finite separable totally and tamely ramified Galois extensions of a local…

We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular we find an asymptotic for the number of abelian field extensions of a number field k whose conductor is the sum of two…

Brumer and Kramer gave bounds on local conductor exponents for an abelian variety $A/\mathbb Q$ in terms of the dimension of $A$ and the localization prime $p$. Here we give improved bounds in the case that $A$ has maximal real…

We show how the ramification filtration on the maximal elementary abelian p-extension (p prime) on a local number field of residual characteristic p can be derived using only Kummer theory and a certain orthogonality relation for the Kummer…

Let $G=(V,E)$ be a finite graph. For $v\in V$ we denote by $G_v$ the subgraph of $G$ that is induced by $v$'s neighbor set. We say that $G$ is $(a,b)$-regular for $a>b>0$ integers, if $G$ is $a$-regular and $G_v$ is $b$-regular for every…

Given a Galois extension $L/K$ of number fields, we describe fine distribution properties of Frobenius elements via invariants from representations of finite Galois groups and ramification theory. We exhibit explicit families of extensions…

We prove that if $f:X \rightarrow A$ is a morphism from a smooth projective variety $X$ to an abelian variety $A$ over a number field $K$, and $G$ is a subgroup of automorphisms of $X$ satisfying certain properties, and if a prime $p$…

Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic…

The well-known Heyde theorem characterizes the Gaussian distributions on the real line by the symmetry of the conditional distribution of one linear form of independent random variables given another. We generalize this theorem to groups of…

Let $L/K$ be a Galois extension of number fields with Galois group $G$. We show that if the density of prime ideals in $K$ that split totally in $L$ tends to $1/|G|$ with a power saving error term, then the density of prime ideals in $K$…

Let $L$ be a finite Galois extension of the number field $K$. We unconditionally bound the least prime ideal of $K$ occurring in the Chebotarev Density Theorem as a power of the discriminant of $L$ with an explicit exponent. We also…

Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence $$1\to Cl_K\to \text{Gal}(H_K/k)\to\text{Gal}(K/k)\to 1$$ by…

We generalize current known distribution results on Shanks--R\'enyi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function…

We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions.…

Given a prime $p$, a number field $\K$ and a finite set of places $S$ of $\K$, let $\K_S$ be the maximal pro-$p$ extension of $\K$ unramified outside $S$. Using the Golod-Shafarevich criterion one can often show that $\K_S/\K$ is infinite.…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

Let $E$ be an elliptic curve defined over the rational numbers and $r$ a fixed integer. Using a probabilistic model consistent with the Chebotarev theorem for the division fields of $E$ and the Sato-Tate distribution, Lang and Trotter…