On Selberg's Lemma For Algebraic Fields
- 1 January 1955
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 7, 138-143
- https://doi.org/10.4153/cjm-1955-016-8
Abstract
1. Introduction. Recently two Japanese authors (1) gave a beautifully simple proof of Selberg's fundamental lemma in the theory of distribution of primes. The proof is based on a curious twist in the Möbius inversion formula. The object of this note is to show that their proof may be extended to a proof of the result for algebraic fields corresponding to Selberg's lemma. Shapiro (2) has already derived this result using Selberg's methods and deduced as a consequence the prime ideal theorem.Keywords
This publication has 2 references indexed in Scilit:
- On Selberg's elementary proof of the prime-number theoremProceedings of the Japan Academy, Series A, Mathematical Sciences, 1951
- An elementary proof of the prime ideal theoremCommunications on Pure and Applied Mathematics, 1949