Functiones et Approximatio Commentarii Mathematici

Euclidean proofs for function fields

Thomas Lachmann

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Abstract

Schur proved the infinitude of primes in arithmetic progressions of the form $\equiv l\mod m$, such that $l^{2}\equiv1\mod m$, 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 $\mathbb{F}_{q}[T]$.

Article information

Source
Funct. Approx. Comment. Math., Volume 58, Number 1 (2018), 105-116.

Dates
First available in Project Euclid: 24 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1521856853

Digital Object Identifier
doi:10.7169/facm/1652

Mathematical Reviews number (MathSciNet)
MR3780037

Zentralblatt MATH identifier
06924919

Subjects
Primary: 11R02

Keywords
Euclidean proof function fields Carlitz module

Citation

Lachmann, Thomas. Euclidean proofs for function fields. Funct. Approx. Comment. Math. 58 (2018), no. 1, 105--116. doi:10.7169/facm/1652. https://projecteuclid.org/euclid.facm/1521856853


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