Division points of Drinfeld modules and special values of Weil 𝐿-functions

1999 ◽  
pp. 31-40
Author(s):  
Zesen Chen
Keyword(s):  
Drinfeld Modules ◽  
Special Values

Cryptanalysis of a cryptosystem based on Drinfeld modules

2006 ◽  
Vol 153 (1) ◽  
pp. 12
Author(s):  
S.R. Blackburn ◽  
C.F.A. Cid ◽  
S.D. Galbraith
Keyword(s):  
Drinfeld Modules

scholarly journals Cogalois theory and drinfeld modules

2019 ◽  
Vol 19 (01) ◽  
pp. 2050001
Author(s):  
Marco Antonio Sánchez–Mirafuentes ◽  
Julio Cesar Salas–Torres ◽  
Gabriel Villa–Salvador
Keyword(s):  
Class Number ◽  
Present Form ◽  
Drinfeld Modules ◽  
Carlitz Module ◽  
Rank One

In this paper, we generalize the results of [M. Sánchez-Mirafuentes and G. Villa–Salvador, Radical extensions for the Carlitz module, J. Algebra 398 (2014) 284–302] to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension [Formula: see text].

Special Values of L-Series

1992 ◽  
Vol 114 (2) ◽  
pp. 337 ◽  
Author(s):  
Rhonda L. Hatcher
Keyword(s):  
Special Values

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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