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• W3135061428 endingPage "106658" @default.
• W3135061428 startingPage "106658" @default.
• W3135061428 abstract "We prove the existence of the maximal real subfields of cyclotomic extensions over the rational function field k=Fq(T) whose class groups can have arbitrarily large ℓn-rank, where Fq is the finite field of prime power order q. We prove this in a constructive way: we explicitly construct infinite families of the maximal real subfields k(Λ)+ of cyclotomic function fields k(Λ) whose ideal class groups have arbitrary ℓn-rank for n = 1, 2, and 3, where ℓ is a prime divisor of q−1. We also obtain a tower of cyclotomic function fields Ki whose maximal real subfields have ideal class groups of ℓn-ranks getting increased as the number of the finite places of k which are ramified in Ki get increased for i≥1. Our main idea is to use the Kummer extensions over k which are subfields of k(Λ)+, where the infinite prime ∞ of k splits completely. In fact, we construct the maximal real subfields k(Λ)+ of cyclotomic function fields whose class groups contain the class groups of our Kummer extensions over k. We demonstrate our results by presenting some examples calculated by MAGMA at the end." @default.
• W3135061428 created "2021-03-15" @default.
• W3135061428 creator A5004482865 @default.
• W3135061428 creator A5022162451 @default.
• W3135061428 date "2021-09-01" @default.
• W3135061428 modified "2023-10-16" @default.
• W3135061428 title "Infinite families of cyclotomic function fields with any prescribed class group rank" @default.
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• W3135061428 doi "https://doi.org/10.1016/j.jpaa.2020.106658" @default.
• W3135061428 hasPublicationYear "2021" @default.
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