scholarly journals Two extension theorems. Modular functions on complemented lattices

2002 ◽  
Vol 52 (1) ◽  
pp. 55-74 ◽  
Author(s):  
Hans Weber
Keyword(s):  
Modular Functions ◽  
Extension Theorems ◽  
Complemented Lattices

Friedrichs type extension theorems for multivalued operators

1991 ◽  
Vol 2 (1) ◽  
pp. 105-121
Author(s):  
George Dinca ◽  
Daniel Mateescu
Keyword(s):  
Extension Theorems ◽  
Multivalued Operators

scholarly journals Algebraic independence of certain numbers related to modular functions

2012 ◽  
Vol 47 (1) ◽  
pp. 121-141
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Algebraic Independence ◽  
Modular Functions

scholarly journals PARAMETRIZING ELLIPTIC CURVES BY MODULAR UNITS

2015 ◽  
Vol 100 (1) ◽  
pp. 33-41 ◽  
Author(s):  
FRANÇOIS BRUNAULT
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Recent Work ◽  
Short Note ◽  
Torsion Subgroup ◽  
Modular Functions ◽  
Open Questions ◽  
Modular Units

It is well known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over $\mathbf{Q}$ can be parametrized by modular units. This answers a question raised by W. Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves $E$ of conductor up to 1000 parametrized by modular units supported in the rational torsion subgroup of $E$. Finally, we raise several open questions.

General Extension Theorems for Linear Functionals

1974 ◽  
Vol 61 (1) ◽  
pp. 111-122 ◽  
Author(s):  
M. Landsberg ◽  
W. Schirotzek
Keyword(s):  
Linear Functionals ◽  
Extension Theorems

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

Sign in / Sign up

Export Citation Format

Share Document