English

Splitting primes

History and Overview 2011-03-16 v3

Abstract

We give an elementary introduction, through illustrative examples but without proofs, to one of the basic consequences of the Langlands programme, namely the law governing the primes modulo which a given irreducible integral polynomial splits completely. Some recent results, such as the modularity of elliptic curves over the rationals, or the proof of Serre's conjecture by Khare and Wintenberger, are also illustrated through examples.

Keywords

Cite

@article{arxiv.1007.4426,
  title  = {Splitting primes},
  author = {Chandan Singh Dalawat},
  journal= {arXiv preprint arXiv:1007.4426},
  year   = {2011}
}

Comments

16 pages, more examples

R2 v1 2026-06-21T15:52:57.684Z