Cyclotomic Fields

2021 ◽  
pp. 109-122
Author(s):  
J. S. Chahal
Keyword(s):  
Cyclotomic Fields

scholarly journals A GENERALISED KUMMER'S CONJECTURE

2010 ◽  
Vol 52 (3) ◽  
pp. 453-472 ◽  
Author(s):  
M. J. R. MYERS
Keyword(s):  
Natural Number ◽  
Class Numbers ◽  
Cyclotomic Fields ◽  
Rate Of Growth ◽  
Relative Class ◽  
Almost All

AbstractKummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott–Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.

scholarly journals Algorithms for solving linear systems over cyclotomic fields

2010 ◽  
Vol 45 (9) ◽  
pp. 902-917 ◽  
Author(s):  
Liang Chen ◽  
Michael Monagan
Keyword(s):  
Linear Systems ◽  
Cyclotomic Fields

scholarly journals On the Hilbert symbol in cyclotomic fields

2002 ◽  
Vol 105 (1) ◽  
pp. 35-49
Author(s):  
Charles Helou
Keyword(s):  
Cyclotomic Fields ◽  
Hilbert Symbol

scholarly journals On p-adic L-functions and cyclotomic fields. II

1977 ◽  
Vol 67 ◽  
pp. 139-158 ◽  
Author(s):  
Ralph Greenberg
Keyword(s):  
Galois Extension ◽  
Additive Group ◽  
Roots Of Unity ◽  
Cyclotomic Fields ◽  
Representation Spaces

Let p be a prime. If one adjoins to Q all pn-th roots of unity for n = 1,2,3, …, then the resulting field will contain a unique subfield Q∞ such that Q∞ is a Galois extension of Q with Gal (Q∞/Q) Zp, the additive group of p-adic integers. We will denote Gal (Q∞/Q) by Γ. In a previous paper [6], we discussed a conjecture relating p-adic L-functions to certain arithmetically defined representation spaces for Γ. Now by using some results of Iwasawa, one can reformulate that conjecture in terms of certain other representation spaces for Γ. This new conjecture, which we believe may be more susceptible to generalization, will be stated below.

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