Chebotarëv and his density theorem

  title={Chebotar{\"e}v and his density theorem},
  author={Peter Stevenhagen and Hendrik W. Lenstra},
  journal={The Mathematical Intelligencer},
The Russian mathematician Nikolăı Grigor′evich Chebotarëv (1894–1947) is famous for his density theorem in algebraic number theory. His centenary was commemorated on June 15, 1994, at the University of Amsterdam. The present paper is based on two lectures that were delivered on that occasion, and its content is summarized by the titles of those lectures: ‘Life and work of Chebotarev’, and ‘Chebotarev’s density theorem for the layman’. An appendix to the paper provides a modern proof of the… 
On Chebotarëv's nonvanishing minors theorem and the Biró-Meshulam-Tao discrete uncertainty principle
A generalization of the Biro-Meshulam-Tao uncertainty principle is established to functions with symmetries that arise from certain group actions, with some of the simplest examples being even and odd functions.
18.785 F2019 Lecture 28: Global class field theory and the Chebotarev density theorem
where v ranges over the places of K (equivalence classes of absolute values), Kv denotes the completion of K at v, and Ov is the valuation ring of Kv if v is nonarchimedean, and equal to Kv
Simple proof of Chebotarev's theorem
We give a simple proof of Chebotarëv’s theorem: Let p be a prime and ω a primitive pth root of unity. Then all minors of the matrix ( ω ij )p−1 i,j=0 are non-zero. Let p be a prime and ω a primitive
Artin reciprocity and
Emil Artin was born on March 3, 1898 in Vienna, as the son of an art dealer and an opera singer, and he died on December 20, 1962 in Hamburg. He was one of the founding fathers of modern algebra. Van
On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity'
Idempotents in complex group rings: theorems of Zalesskii and Bass revisited
Let be a group, and let C be the group ring of over C. We rst give a simplied and self-contained proof of Zalesskii's theorem (23) that the canonical trace on C takes rational values on idempotents.
Dedekind Zeta Zeroes and Faster Complex Dimension Computation
A minimalist hypothesis is derived that allows failures of GRH but still enable complex dimension computation in the polynomial hierarchy, and more plausible hypotheses are explored yielding the same speed-up.
An introduction to Skolem ’ s p-adic method for solving Diophantine equations Josha Box July 3 ,
In this thesis, an introduction to Skolem’s p-adic method for solving Diophantine equations is given. The main theorems that are proven give explicit algorithms for computing bounds for the amount of
Simple proof of Chebotarev's theorem on roots of unity
We give a simple proof of Chebotarev's theorem: Let $p$ be a prime and $\omega $ a primitive $p$th root of unity. Then all minors of the matrix $(\omega^{ij})_{i,j=0}^{p-1}$ are non-zero.
On a Class of Lacunary Almost Newman Polynomials Modulo P and Density Theorems
Abstract The reduction modulo p of a family of lacunary integer polynomials, associated with the dynamical zeta function ζβ(z)of the β-shift, for β> 1 close to one, is investigated. We briefly recall


Algebraic Number Theory
This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary
Abelian L-adic representation and elliptic curves
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent
Class Field Theory
I. Group and Field Theoretic Foundations.- 1. Infinite Galois Theory.- 2. Profinite Groups.- 3. G-Modules.- 4. The Herbrand Quotient.- 5. Kummer Theory.- II. General Class Field Theory.- 1. Frobenius
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe
In seiner Arbeit Uber die Irreductibilitat von Gleichungen (Sitzungsber. 1880, S. 155) hat Kronecker folgenden Satz entwickelt:
Quelques applications du théorème de densité de Chebotarev
The present invention relates to multinozzle spraying apparatus for spraying insecticides and the like. A plurality of spray nozzles having differing spray characteristics are provided attached to a
A history of Greek mathematics
A text which looks at the history of Greek mathematics - a subject on which the author established a special authority by his succession of works on Diophantus, Apolonius of Perga, Archimedes, Euclid
Vier neue mondförmige Flächen, deren Inhalt quadrirbar ist.
Von Hippocrates haben wir schon den Ausdruck des Flächen -Inhalts einer von zwei Kreisbogen begränzten Figur: es scheint mir merkwürdig, dafs man noch nicht mehrere gesucht hat. Es lassen sich leicht
Uber eine neue Art von L-Reihen
A semi-automatic palletizer is disclosed providing an elevator for positioning pallets below an arranging table to receive layers of arranged articles. As each layer is positioned on a pallet
Über den Tschebotareffschen Dichtigkeitssatz