Quadratic fields with cyclic 2-class groups

2012/11/12 by Dominguez, Carlos, Miller, Steven J., Wong, Siman
#11R29 (Primary) 11P55 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1211.2605

Abstract

For any integer k≥ 1, we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order 2^k. The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class to be a square.

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