The Chebotarev density theorem for a number field

2016 ◽  
pp. 25-40
Keyword(s):  
Number Field ◽  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals An explicit Chebotarev density theorem under GRH

2019 ◽  
Vol 200 ◽  
pp. 441-485 ◽  
Author(s):  
Loïc Grenié ◽  
Giuseppe Molteni
Keyword(s):  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals A bound for the least prime ideal in the Chebotarev Density Theorem

1979 ◽  
Vol 54 (3) ◽  
pp. 271-296 ◽  
Author(s):  
J. C. Lagarias ◽  
H. L. Montgomery ◽  
A. M. Odlyzko
Keyword(s):  
Prime Ideal ◽  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals Knots which behave like the prime numbers

2013 ◽  
Vol 149 (8) ◽  
pp. 1235-1244 ◽  
Author(s):  
Curtis T. McMullen
Keyword(s):  
Number Fields ◽  
Prime Numbers ◽  
Density Theorem ◽  
Chebotarev Density Theorem

AbstractThis paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.

scholarly journals On the moments of torsion points modulo primes and their applications

2020 ◽  
pp. 1-17
Author(s):  
Amir Akbary ◽  
Peng-Jie Wong
Keyword(s):  
Algebraic Group ◽  
Algebraic Groups ◽  
Residue Field ◽  
Density Theorem ◽  
Polynomial Equations ◽  
Absolute Galois Group ◽  
Torsion Points ◽  
Chebotarev Density Theorem ◽  
System Of Polynomial Equations ◽  
Dimension One

Let [Formula: see text] be the group of [Formula: see text]-torsion points of a commutative algebraic group [Formula: see text] defined over a number field [Formula: see text]. For a prime [Formula: see text] of [Formula: see text], we let [Formula: see text] be the number of [Formula: see text]-solutions of the system of polynomial equations defining [Formula: see text] when reduced modulo [Formula: see text]. Here, [Formula: see text] is the residue field at [Formula: see text]. Let [Formula: see text] denote the number of primes [Formula: see text] of [Formula: see text] such that [Formula: see text]. We then, for algebraic groups of dimension one, compute the [Formula: see text]th moment limit [Formula: see text] by appealing to the Chebotarev density theorem. We further interpret this limit as the number of orbits of the action of the absolute Galois group of [Formula: see text] on [Formula: see text] copies of [Formula: see text] by an application of Burnside’s Lemma. These concrete examples suggest a possible approach for determining the number of orbits of a group acting on [Formula: see text] copies of a set.

A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS

2018 ◽  
Vol 98 (2) ◽  
pp. 196-202
Author(s):  
STEVE MEAGHER
Keyword(s):  
Conjugacy Class ◽  
Finite Fields ◽  
Simple Proof ◽  
Function Fields ◽  
Rational Points ◽  
Density Theorem ◽  
Chebotarev Density Theorem ◽  
Projective Varieties

We present a simple proof of the Chebotarev density theorem for finite morphisms of quasi-projective varieties over finite fields following an idea of Fried and Kosters for function fields. The key idea is to interpret the number of rational points with a given Frobenius conjugacy class as the number of rational points of a twisted variety, which is then bounded by the Lang–Weil estimates.

scholarly journals A unified and improved Chebotarev density theorem

2019 ◽  
Vol 13 (5) ◽  
pp. 1039-1068
Author(s):  
Jesse Thorner ◽  
Asif Zaman
Keyword(s):  
Density Theorem ◽  
Chebotarev Density Theorem
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