# Euclidean proofs for function fields

Thomas Lachmann

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

Schur proved the infinitude of primes in arithmetic progressions of the form ≡ l mod m, such that L2 ≡ 1 mod m, with non-analytic methods by ideas inspired from the famous proof Euclid gave for the infinitude of primes. Ram Murty showed that Schur’s method has its limits given by the assumption Schur made. We will discuss analogous for the primes in the ring Fq[T].

Original language English 105-116 12 Functiones et Approximatio, Commentarii Mathematici 58 1 https://doi.org/10.7169/facm/1652 Published - 1 Mar 2018

### Fingerprint

Function Fields
Euclidean
Euclid
Arithmetic sequence
Ring

### Keywords

• Carlitz module
• Euclidean proof
• Function fields

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Euclidean proofs for function fields. / Lachmann, Thomas.

In: Functiones et Approximatio, Commentarii Mathematici, Vol. 58, No. 1, 01.03.2018, p. 105-116.

Research output: Contribution to journalArticleResearchpeer-review

Lachmann, Thomas. / Euclidean proofs for function fields. In: Functiones et Approximatio, Commentarii Mathematici. 2018 ; Vol. 58, No. 1. pp. 105-116.
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