scholarly journals Potential Automorphy of Odd-Dimensional Symmetric Powers of Elliptic Curves and Applications

2009 ◽  
pp. 1-21 ◽  
Author(s):  
Michael Harris
Keyword(s):  
Elliptic Curves ◽  
Symmetric Powers

scholarly journals Iwasawa μ-invariants of elliptic curves and their symmetric powers

2003 ◽  
Vol 102 (2) ◽  
pp. 191-213 ◽  
Author(s):  
Michael J. Drinen
Keyword(s):  
Elliptic Curves ◽  
Symmetric Powers

scholarly journals Euler Factors and Local Root Numbers for Symmetric Powers of Elliptic Curves

2009 ◽  
Vol 5 (4) ◽  
pp. 1311-1341
Author(s):  
Neil Dummigan ◽  
Phil Martin ◽  
Mark Watkins
Keyword(s):  
Elliptic Curves ◽  
Symmetric Powers ◽  
Root Numbers ◽  
Local Root ◽  
Local Root Numbers

scholarly journals On the potential automorphy of certain odd-dimensional Galois representations

2010 ◽  
Vol 146 (3) ◽  
pp. 607-620 ◽  
Author(s):  
Thomas Barnet-Lamb
Keyword(s):  
Elliptic Curves ◽  
Galois Representations ◽  
Symmetric Powers

AbstractIn a previous paper, the potential automorphy of certain Galois representations to GLn for n even was established, following the work of Harris, Shepherd–Barron and Taylor and using the lifting theorems of Clozel, Harris and Taylor. In this paper, we extend those results to n=3 and n=5, and conditionally to all other odd n. The key additional tools necessary are results which give the automorphy or potential automorphy of symmetric powers of elliptic curves, most notably those of Gelbert, Jacquet, Kim, Shahidi and Harris.

scholarly journals Quadratic points on non-split Cartan modular curves

2021 ◽  
pp. 1-23
Author(s):  
Philippe Michaud-Rodgers
Keyword(s):  
Elliptic Curves ◽  
Rational Points ◽  
Quadratic Fields ◽  
Modular Curves ◽  
Symmetric Powers

In this paper, we study quadratic points on the non-split Cartan modular curves [Formula: see text], for [Formula: see text] and [Formula: see text]. Recently, Siksek proved that all quadratic points on [Formula: see text] arise as pullbacks of rational points on [Formula: see text]. Using similar techniques for [Formula: see text], and employing a version of Chabauty for symmetric powers of curves for [Formula: see text], we show that the same holds for [Formula: see text] and [Formula: see text]. As a consequence, we prove that certain classes of elliptic curves over quadratic fields are modular.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

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