JournalspmVol. 73, No. 1pp. 65–70

Generators of finite fields with powers of trace zero and cyclotomic function fields

  • José Felipe Voloch

    University of Texas at Austin, USA
Generators of finite fields with powers of trace zero and cyclotomic function fields cover
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Abstract

In this paper, we count the number of generators of finite fields with powers of trace zero up to some point, answering a question of Z. Reichstein. More generally, we count irreducible polynomials over finite fields with some prescribed coefficients. This is done by relating this count to the problem of counting rational points on curves over finite fields whose function fields are subfields of cyclotomic function fields.

Cite this article

José Felipe Voloch, Generators of finite fields with powers of trace zero and cyclotomic function fields. Port. Math. 73 (2016), no. 1, pp. 65–70

DOI 10.4171/PM/1976