A Numerical Survey of the Reduction of Modular Curve Genus by Fricke’s Involutions

Number Theory ◽  
1991 ◽  
pp. 85-104 ◽  
Author(s):  
Harvey Cohn
Keyword(s):  
Modular Curve ◽  
Curve Genus

Zeta functions of twisted modular curves

2006 ◽  
Vol 80 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Cristian Virdol
Keyword(s):  
Zeta Function ◽  
Galois Group ◽  
Complex Plane ◽  
Zeta Functions ◽  
Modular Curves ◽  
Absolute Galois Group ◽  
Modular Curve ◽  
The Absolute

AbstractIn this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.

Remarks on ample vector bundles of curve genus two

2007 ◽  
Vol 88 (5) ◽  
pp. 419-424 ◽  
Author(s):  
Hidetoshi Maeda
Keyword(s):  
Vector Bundles ◽  
Curve Genus ◽  
Genus Two

On the modular curve X0(23)

2012 ◽  
pp. 317-345 ◽  
Author(s):  
René Schoof
Keyword(s):  
Modular Curve

Automorphisms of the Modular Curve

2005 ◽  
pp. 25-37 ◽  
Author(s):  
Peter Bending ◽  
Alan Camina ◽  
Robert Guralnick
Keyword(s):  
Modular Curve

Rational torsion of generalized Jacobians of modular and Drinfeld modular curves

2019 ◽  
Vol 31 (3) ◽  
pp. 647-659
Author(s):  
Fu-Tsun Wei ◽  
Takao Yamazaki
Keyword(s):  
Prime Power ◽  
Analogous Result ◽  
Power Level ◽  
Modular Curves ◽  
Generalized Jacobian ◽  
Torsion Points ◽  
Modular Curve ◽  
Generalized Jacobians ◽  
Drinfeld Modular Curves ◽  
Primary Torsion

Abstract We consider the generalized Jacobian {\widetilde{J}} of the modular curve {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the {\mathbb{Q}} -rational torsion points on {\widetilde{J}} up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on {\widetilde{J}} and its Eisenstein property.

Ample Vector Bundles of Curve Genus One

1999 ◽  
Vol 42 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Antonio Lanteri ◽  
Hidetoshi Maeda
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Ample Vector Bundle ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Curve Genus ◽  
Genus One ◽  
Complex Projective ◽  
Zero Locus

AbstractWe investigate the pairs (X, ε) consisting of a smooth complex projective variety X of dimension n and an ample vector bundle ε of rank n − 1 on X such that ε has a section whose zero locus is a smooth elliptic curve.

scholarly journals Functions and differentials on the non-split Cartan modular curve of level 11

2016 ◽  
Vol 86 (303) ◽  
pp. 437-454
Author(s):  
Julio Fernández ◽  
Josep González
Keyword(s):  
Modular Curve

scholarly journals NORMAL BASES FOR MODULAR FUNCTION FIELDS

2017 ◽  
Vol 95 (3) ◽  
pp. 384-392
Author(s):  
JA KYUNG KOO ◽  
DONG HWA SHIN ◽  
DONG SUNG YOON
Keyword(s):  
Galois Extension ◽  
Meromorphic Functions ◽  
Function Fields ◽  
Modular Function ◽  
Normal Basis ◽  
Modular Curve ◽  
Normal Bases ◽  
Free Element

We provide a concrete example of a normal basis for a finite Galois extension which is not abelian. More precisely, let $\mathbb{C}(X(N))$ be the field of meromorphic functions on the modular curve $X(N)$ of level $N$. We construct a completely free element in the extension $\mathbb{C}(X(N))/\mathbb{C}(X(1))$ by means of Siegel functions.

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