scholarly journals On the refined class number formula for global function fields

2004 ◽  
Vol 11 (5) ◽  
pp. 583-587 ◽  
Author(s):  
Joongul Lee
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Global Function ◽  
Global Function Fields ◽  
Class Number Formula ◽  
Number Formula

Elliptic Units and Class Fields of Global Function Fields

1997 ◽  
Vol 40 (4) ◽  
pp. 385-394
Author(s):  
Sunghan Bae ◽  
Pyung-Lyun Kang
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Global Function ◽  
Global Function Fields ◽  
Class Fields ◽  
Elliptic Units

AbstractElliptic units of global function fields were first studied by D. Hayes in the case that deg ∞ is assumed to be 1, and he obtained some class number formulas using elliptic units. We generalize Hayes’ results to the case that deg ∞ is arbitrary.

scholarly journals Class number formulae in the form of a product of determinants in function fields

2005 ◽  
Vol 78 (2) ◽  
pp. 227-238 ◽  
Author(s):  
Jaehyun Ahn ◽  
Soyoung Choi ◽  
Hwanyup Jung
Keyword(s):  
Class Number ◽  
Prime Power ◽  
Function Fields ◽  
The Real ◽  
Relative Class ◽  
Intermediate Field ◽  
Class Number Formula ◽  
Relative Class Number ◽  
Number Formula

AbstractIn this paper, we generalize the Kučera's group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.

scholarly journals On S-class number relations of algebraic tori in Galois extensions of global fields

1991 ◽  
Vol 124 ◽  
pp. 133-144 ◽  
Author(s):  
Masanori Morishita
Keyword(s):  
Class Number ◽  
Quadratic Forms ◽  
Euler Number ◽  
Number Fields ◽  
Binary Quadratic Forms ◽  
Algebraic Number Fields ◽  
Algebraic Tori ◽  
Genus Theory ◽  
Class Number Formula ◽  
Number Formula

As an interpretation and a generalization of Gauss’ genus theory on binary quadratic forms in the language of arithmetic of algebraic tori, Ono [02] established an equality between a kind of “Euler number E(K/k)” for a finite Galois extension K/k of algebraic number fields and other arithmetical invariants associated to K/k. His proof depended on his Tamagawa number formula [01] and Shyr’s formula [Sh] which follows from the analytic class number formula of a torus. Later, two direct proofs were given by Katayama [K] and Sasaki [Sa].

IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE

2008 ◽  
Vol 17 (10) ◽  
pp. 1199-1221 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YASUSHI MIZUSAWA
Keyword(s):  
Number Field ◽  
Class Number ◽  
Homology Sphere ◽  
Rational Homology ◽  
Homology Groups ◽  
Cyclic Covers ◽  
Class Number Formula ◽  
Number Formula ◽  
Iwasawa Invariants ◽  
Rational Homology Sphere

Based on the analogy between links and primes, we present an analogue of the Iwasawa's class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.

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