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math.NT2018
A Note on the equivalence of the parity of class numbers and the signature ranks of units in cyclotomic fields
David S. Dummit
We collect some statements regarding equivalence of the parities of various class numbers and signature ranks of units in prime power cyclotomic fields. We correct some misstatemen…
math.NT2018
Classes of order 4 in the strict class group of number fields and remarks on unramified quadratic extensions of unit type
David S. Dummit
Let be a number field of degree over . Then the 4-rank of the strict class group of is at least ${\text{rank}_2 \, } ({ E_{K}^{+} } / E_K^2) - \lfloor n /2…
math.NT2018
Signature Ranks of Units in Cyclotomic Extensions of Abelian Number Fields
David S. Dummit, Evan P. Dummit, Hershy Kisilevsky
We prove the rank of the group of signatures of the circular units (hence also the full group of units) of tends to infinity with . We also show the signat…