On an extension of Mazur's theorem on Lipschitz functions

1994 ◽  
Vol 63 (6) ◽  
pp. 535-540
Author(s):  
S. Rolewicz
Keyword(s):  
Lipschitz Functions ◽  
Mazur’S Theorem

scholarly journals Mazur’s rational torsion result for pointless genus one curves: examples

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Arjan Dwarshuis ◽  
Majken Roelfszema ◽  
Jaap Top
Keyword(s):  
Algebraic Geometry ◽  
Elliptic Curves ◽  
Rational Point ◽  
Torsion Points ◽  
Arbitrary Genus ◽  
Mazur’S Theorem ◽  
Genus One

AbstractThis note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over $$\mathbb {Q}$$ Q in a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point. The main result is that explicit examples are provided of ‘pointless’ genus one curves over $$\mathbb {Q}$$ Q corresponding to the torsion orders 7, 8, 9, 10, 12 (and hence, all possibilities) occurring in Mazur’s theorem. In fact three distinct methods are proposed for constructing such examples, each involving different in our opinion quite nice ideas from the arithmetic of elliptic curves or from algebraic geometry.

On two simple decompositions of Lipschitz functions

Optimization ◽  
2008 ◽  
Vol 57 (2) ◽  
pp. 249-261 ◽  
Author(s):  
S. Zlobec
Keyword(s):  
Lipschitz Functions

Fourier-Bessel Dini Lipschitz functions in the space $$L_{\alpha ,n}^{2}$$ L α , n 2

2017 ◽  
Vol 28 (7-8) ◽  
pp. 1157-1165 ◽  
Author(s):  
S. El Ouadih ◽  
R. Daher
Keyword(s):  
Lipschitz Functions
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