Modular Functions of One Variable IV

1975 ◽  
Keyword(s):  
Modular Functions

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.

scholarly journals Modular functions arising from some finite groups

1981 ◽  
Vol 37 (156) ◽  
pp. 547-547 ◽  
Author(s):  
Larissa Queen
Keyword(s):  
Finite Groups ◽  
Modular Functions

A Note on Weierstrass Points

1967 ◽  
Vol 19 ◽  
pp. 268-272 ◽  
Author(s):  
Donald L. McQuillan
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Function Fields ◽  
Algebraic Function ◽  
Modular Functions ◽  
Weierstrass Points ◽  
Algebraic Function Fields

In (4) G. Lewittes proved some theorems connecting automorphisms of a compact Riemann surface with the Weierstrass points of the surface, and in (5) he applied these results to elliptic modular functions. We refer the reader to these papers for definitions and details. It is our purpose in this note to point out that these results are of a purely algebraic nature, valid in arbitrary algebraic function fields of one variable over algebraically closed ground fields (with an obvious restriction on the characteristic). We shall also make use of the calculation carried out in (5) to obtain a rather easy extension of a theorem proved in (6, p. 312).

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