scholarly journals The Farey density of norm subgroups of global fields (II)

1977 ◽  
Vol 18 (1) ◽  
pp. 57-67
Author(s):  
S. D. Cohen ◽  
R. W. K. Odoni
Keyword(s):  
Algebraic Number ◽  
Function Fields ◽  
Rational Functions ◽  
Number Fields ◽  
Ground Field ◽  
Algebraic Number Fields ◽  
Global Fields ◽  
Finite Constant

In this paper we shall derive for function fields in one variable over finite constant fields results analogous to [1], where algebraic number fields were considered. The ground field P will be the set of all rational functions in a given transcendent X, with coefficients in k = GF(q), q = pr, p a prime; thus P = k(X).

On a certain analogy between algebraic number fields and function fields

2001 ◽  
pp. 512-515
Author(s):  
Ichiro Satake ◽  
Genjiro Fujisaki ◽  
Kazuya Kato ◽  
Masato Kurihara ◽  
Shoichi Nakajima
Keyword(s):  
Algebraic Number ◽  
Function Fields ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
And Function

scholarly journals Approximation in algebraic function fields of one variable

1967 ◽  
Vol 7 (3) ◽  
pp. 341-355 ◽  
Author(s):  
John Coates
Keyword(s):  
Algebraic Number ◽  
Function Fields ◽  
Algebraic Function ◽  
Number Fields ◽  
Geometry Of Numbers ◽  
Algebraic Number Fields ◽  
Algebraic Function Fields ◽  
Quantitative Results

In his paper (4), Mahler established several strong quantitative results on approximation in algebraic number fields using the geometry of numbers. In the present paper I derive analogous results for algebraic function fields of one variable using an analogue of the geometry of numbers.

scholarly journals A Note on Units of Algebraic Number Fields

1955 ◽  
Vol 9 ◽  
pp. 115-118 ◽  
Author(s):  
Tomio Kubota
Keyword(s):  
Existence Theorem ◽  
Algebraic Number ◽  
Present Note ◽  
Number Fields ◽  
Algebraic Number Fields

We shall prove in the present note a theorem on units of algebraic number fields, applying one of the strongest formulations, be Hasse [3], of Grunwald’s existence theorem.

scholarly journals K-RATIONAL D-BRANE CRYSTALS

2012 ◽  
Vol 27 (22) ◽  
pp. 1250112
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
String Theory ◽  
Algebraic Number ◽  
Special Class ◽  
Building Blocks ◽  
Number Fields ◽  
Central Point ◽  
Algebraic Number Fields ◽  
Special Values ◽  
Toroidal Compactifications ◽  
Base Points

In this paper the problem of constructing space–time from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of certain Calabi–Yau varieties. The collections of D-branes involved have algebraic base points, leading to the notion of K-arithmetic D-crystals for algebraic number fields K. This idea can be tested for D0-branes in the framework of toroidal compactifications via the conjectures of Birch and Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these conjectures can be interpreted as formulae that relate the canonical Néron–Tate height of the base points of the D-crystals to special values of the motivic L-function at the central point. In simple cases the knowledge of the D-crystals of Heegner type suffices to uniquely determine the geometry.

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