cyclic cubic fields
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2021 ◽  
pp. 1-12
Author(s):  
Nigel Boston ◽  
Michael R. Bush


2021 ◽  
Vol 44 (2) ◽  
Author(s):  
Tomokazu Kashio ◽  
Ryutaro Sekigawa


2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Peter Bruin ◽  
Maarten Derickx ◽  
Michael Stoll


2018 ◽  
Vol 88 (319) ◽  
pp. 2443-2459 ◽  
Author(s):  
Maarten Derickx ◽  
Filip Najman


2018 ◽  
Vol 14 (02) ◽  
pp. 399-415
Author(s):  
Ha Thanh Nguyen Tran ◽  
Peng Tian

The size function for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the trivial class of Arakelov divisors. This conjecture was proved for many number fields with unit groups of rank one. Our research confirms that the conjecture also holds for cyclic cubic fields, which have unit groups of rank two.



2016 ◽  
Vol 169 ◽  
pp. 86-102 ◽  
Author(s):  
Tommy Hofmann ◽  
Yinan Zhang


2016 ◽  
Vol 167 ◽  
pp. 394-406
Author(s):  
Steve Balady


2014 ◽  
Vol 10 (05) ◽  
pp. 1259-1276
Author(s):  
Simon Rubinstein-Salzedo

This article discusses deviations from the Cohen–Lenstra heuristics when roots of unity are present. In particular, we propose an explanation for the discrepancy between the observed number of cyclic cubic fields whose 2-class group is C2 × C2 and the number predicted by the Cohen–Lenstra heuristics, in terms of an invariant living in a quotient of the Schur multiplier group. We also show that, in some cases, the definition of the invariant can be simplified greatly, and we compute the invariant when the cubic field is ramified at exactly one prime, up to 108.



2007 ◽  
Vol 230 (1) ◽  
pp. 167-183
Author(s):  
Akito Nomura


2006 ◽  
Vol 49 (3) ◽  
pp. 472-480 ◽  
Author(s):  
Alan K. Silvester ◽  
Blair K. Spearman ◽  
Kenneth S. Williams

AbstractThe number of cyclic cubic fields with a given conductor and a given index is determined.



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