3 edition of On the product of the regulator and the class number of the cyclotomic field. found in the catalog.
On the product of the regulator and the class number of the cyclotomic field.
Bibliography: p. 7.
|Series||Turun Yliopyston Julkaisuja. Annales Universitatis Turkuensis. Sarja-series A: I. Astronomica-chemica-physica-mathematica, 118:6|
|LC Classifications||AS262.T84 A27 no. 118:6|
|The Physical Object|
|LC Control Number||79457243|
The formula, in combination with a recent work of Y. One can input the attached bid with generators if the subgroup C is non trivial for B instead of the module itself, saving some time. SPIPconsists in finding a generator resp. See also bnfisnorm. Thiel, C.
See also bnfisnorm. Warning: setting this may induce lengthy computations. For any extensions satisfying the conditions of Lemma 4. Brauer, R.
The maximal abelian p-extension unramified outside p. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. By default, most of the bnf routines depend on the correctness of the GRH. Assume for simplicity that there exists a place [v. In: Johansson, T.
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G Z, [U. For any extensions satisfying the conditions of Lemma 4. Chapter 9 brings together the earlier material through the study of quadratic number fields. Some theorems on class groups. Brauer, R. In the mid 's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt.
In fact: never access a component directly, always use a proper member function. Part of the Universitext book series UTX Abstract Class numbers of cyclotomic fields have been the subject of considerable investigations. Notes Acknowledgments We would like to sincerely thank Claus Fieker for his comments about our implementation.
For each subgroup H of G there is a fibre diagram [Mathematical Expression Omitted] associated to which there is a Mayer-Vietoris sequence cf. It is possible for different groups to have the same name. Smart, N. Fermat's Last Theorem.
G,G,1] has trivial kernel cf. An elegant and complete although not very explicit characterization of the Z[G]-genus of [U.
The Davenport-Hasse Distribution. Shoup, V. But I think that, pedagogically and aesthetically, it is better to give a proof which handles the hardest case in such a way that the other cases are covered at the same time.
The Main Conjecture. Taylor, L-functions and Galois modules notes by D. We need a little more notation. The estimate for hm. The Index for k Even. In: Nguyen, P.This banner text can have markup.
web; books; video; audio; software; images; Toggle navigation. it has class number divisible by 4, and the results of R´edei and Reichardt show that the 4-class ﬁeld of k is generated by the square root of αq = x+ y √ p, where x,y∈Zsatisfy x2 −py2 = −qz2; the same is true with q replaced by q0.
Since both αq and αq0 have mixed signature, their product. The Calculation of a Large Cubic Class Number with an Application to Real Cyclotomic Fields number h3 via the Euler product for q of the class number of the cyclotomic field (exp 2iπ/p.Nov 01, · The diverse scope includes the pdf topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field .Good references on algebraic number theory abound.
Here are some: [C] Cox. David A, Primes of the form x^2 + n y^2 (cover tangentially and provides arithmetic motivation for some material) [F] Frohlich, Algebraic Number Theory [J] Janusz, Algebraic Number Fields.An algebraic number ﬁeld is ebook ﬁnite extension of Q; an alge-braic ebook is an element of an algebraic number ﬁeld.
Alge-braic number theory studies the arithmetic of algebraic number ﬁelds — the ring of integers in the number ﬁeld, the ideals and units in the ring of integers, the extent to which unique factor-ization holds, and so on.