Algebraic Number Theory

1999/01/01 by Jürgen Neukirch · 1,556 citations
Mathematics · #Algebra over a field #Algebraic number #Algebraic number theory #Algebraic theory #Computer science #History and Theory of Mathematics #Mathematics #Pure mathematics

paper · doi:10.1007/978-3-662-03983-0

published in Grundlehren der mathematischen Wissenschaften (Springer Nature)

crossref issued 1999/01/01 · crossref published 1999/01/01 · crossref published-print 1999/01/01 · openalex publication_date 1999/01/01 · crossref created 2013/01/15 · crossref deposited 2019/04/06 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/04

Cited by

• Reconstructing global fields from dynamics in the abelianized Galois group
• Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta-functions, notes on the work of Shinichi Mochizuki
• Seshadri constants, diophantine approximation, and Roth’s theorem for arbitrary varieties
• Functorial properties of generalised Steinberg representations
• A note on divisible points of curves
• Algebraic K-Theory of Rings of Integers in Local and Global Fields
• (1 +i) - ary GCD Computation inZ[ i ]as an Analogue to the Binary GCD Algorithm
• Bounded diagonal orbits in homogeneous spaces over function fields
• On the Galois structure of the class group of certain Kummer extensions
• Base change and K-theory for GL(n,R)
• A solvable counterexample to the Hambleton-Taylor-Williams Conjecture
• On the abc Conjecture in Algebraic Number Fields
• Extended eigenvarieties for overconvergent cohomology
• Squares in \mathbbF_p² and permutations involving primitive roots
• Torsion subgroups in the units of the integral group ring of PSL(2, p 3)
• Ergodic properties of visible lattice points
• Nonvanishing of twists of -functions attached to Hilbert modular forms
• The dualizing module and top-dimensional cohomology group of GL_n(O)
• The Brauer group of the moduli stack of elliptic curves
• A tropical approach to nonarchimedean Arakelov geometry
• p-Selmer growth in extensions of degree p
• Dirichlet Shapes of Unit Lattices and Escape of Mass
• Galois covers of the open p-adic disc
• Metric Mahler measures over number fields
• Every lens space contains a genus one homologically fibered knot
• ON LINEAR COMBINATIONS OF UNITS WITH BOUNDED COEFFICIENTS
• Analysis on arithmetic schemes. II
• Prime number [wikipedia]