scholarly journals A Class Number Relation Over Function Fields

1995 ◽  
Vol 54 (2) ◽  
pp. 318-340 ◽  
Author(s):  
J.K. Yu
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Number Relation

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Prime Degree ◽  
Cyclic Function ◽  
Quadratic Function Fields

AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

scholarly journals Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)

2016 ◽  
Vol 12 (04) ◽  
pp. 853-902 ◽  
Author(s):  
Patrick Morton
Keyword(s):  
Class Number ◽  
Algebraic Function ◽  
Periodic Points ◽  
Imaginary Quadratic Fields ◽  
Class Number Formula ◽  
All Solutions ◽  
Number Formula ◽  
Class Fields ◽  
Fermat Equation ◽  
Number Relation

Explicit solutions of the cubic Fermat equation are constructed in ring class fields [Formula: see text], with conductor [Formula: see text] prime to [Formula: see text], of any imaginary quadratic field [Formula: see text] whose discriminant satisfies [Formula: see text] (mod [Formula: see text]), in terms of the Dedekind [Formula: see text]-function. As [Formula: see text] and [Formula: see text] vary, the set of coordinates of all solutions is shown to be the exact set of periodic points of a single algebraic function and its inverse defined on natural subsets of the maximal unramified, algebraic extension [Formula: see text] of the [Formula: see text]-adic field [Formula: see text]. This is used to give a dynamical proof of a class number relation of Deuring. These solutions are then used to give an unconditional proof of part of Aigner’s conjecture: the cubic Fermat equation has a nontrivial solution in [Formula: see text] if [Formula: see text] (mod [Formula: see text]) and the class number [Formula: see text] is not divisible by [Formula: see text]. If [Formula: see text], congruence conditions for the trace of specific elements of [Formula: see text] are exhibited which imply the existence of a point of infinite order in [Formula: see text].

scholarly journals Function fields of class number one

2015 ◽  
Vol 154 ◽  
pp. 375-379 ◽  
Author(s):  
Qibin Shen ◽  
Shuhui Shi
Keyword(s):  
Class Number ◽  
Function Fields

A class number relation in Frobenius extensions of number fields

Mathematika ◽  
1977 ◽  
Vol 24 (2) ◽  
pp. 216-225 ◽  
Author(s):  
Colin D. Walter
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Number Relation

scholarly journals A combinatorial refinement of the Kronecker-Hurwitz class number relation

2016 ◽  
Vol 145 (3) ◽  
pp. 1003-1008 ◽  
Author(s):  
Alexandru A. Popa ◽  
Don Zagier
Keyword(s):  
Class Number ◽  
Number Relation
Sign in / Sign up

Export Citation Format

Share Document