منابع مشابه
L-functions and Cyclotomic Units
Here RK is the regulator of K, wK is the number of roots of unity in K and hK is the class number of K. This formula is a striking connection between arithmetic and analysis, and there have been many attempts to generalize it to other L-functions: one expects that the value of a “motivic” L-function at an integer point should involve a transcendental factor, a boring rational factor, and an int...
متن کاملCyclotomic Units and the Iwasawa Main Conjecture
In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...
متن کاملA Cohomological Approach to Properties of the Norm Residue Symbol in Higher Dimensional Class Eld Theory
In earlier work the author proved that the Vostokov symbol of the n-dimensional mixed characteristic local eld X n = kfft 1 n) q ! q commutes with the corresponding Vostokov symbol of X n?1 = kfft 1 gg : : :fft n?2 gg. Here the author generalizes this theorem to the case of a regular local ring A subject to certain conditions. This is done by using Kato's reformulation of the Vostokov symbol as...
متن کاملA Method to Solve Cyclotomic Norm Equations
We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ f̄ in the totally real field Q(ζp + ζ −1 p ). The classical method of solving this problem involves finding generators of principal ideals by enumerating the whole class group associated with Q(ζp), but this approach quickly becomes infeasible as p increases. The apparent h...
متن کاملCalculating the Power Residue Symbol and Ibeta
In the recent PhD thesis of Bouw, an algorithm is examined that computes the group structure of the principal units of a p-adic number eld completion. In the same thesis, this algorithm is used to compute Hilbert norm residue symbols. In the present paper, we will demonstrate two other applications. e rst application is the computation of an important invariant of number eld completions, ca...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1995
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-73-2-147-188