On subfields of the second generalization of the GK maximal function\n field

2018/10/31 by Peter Beelen, Beelen, Peter, Maria Montanucci +1
Arts and Humanities · Mathematics · Social Sciences · #11G20 #14H25 #14H37 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1811.00049

openalex publication_date 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The second generalized GK function fields K_n are a recently found family\nof maximal function fields over the finite field with q²ⁿ elements, where\nq is a prime power and n \≥ 1 an odd integer. In this paper we construct\nmany new maximal function fields by determining various Galois subfields of\nK_n. In case \gcd(q+1,n)=1 and either q is even or q \≡ 1 pmod4,\nwe find a complete list of Galois subfields of K_n. Our construction adds\nseveral previously unknown genera to the genus spectrum of maximal curves.\n

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