Geometric Modular Forms and Elliptic Curves

10.1142/8277 ◽  
2011 ◽  
Author(s):  
Haruzo Hida
Keyword(s):  
Elliptic Curves ◽  
Modular Forms

scholarly journals Quasi-modular forms attached to elliptic curves, I

2012 ◽  
Vol 19 (2) ◽  
pp. 307-377 ◽  
Author(s):  
Hossein Movasati
Keyword(s):  
Elliptic Curves ◽  
Modular Forms

scholarly journals Higher reciprocity law, modular forms of weight 1 and elliptic curves

1985 ◽  
Vol 98 ◽  
pp. 109-115 ◽  
Author(s):  
Masao Koike
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Cusp Forms ◽  
Close Connection ◽  
Irreducible Polynomials ◽  
Reciprocity Law

In this paper, we study higher reciprocity law of irreducible polynomials f(x) over Q of degree 3, especially, its close connection with elliptic curves rational over Q and cusp forms of weight 1. These topics were already studied separately in a special example by Chowla-Cowles [1] and Hiramatsu [2]. Here we bring these objects into unity.

scholarly journals Elliptic curves, modular forms, and sums of Hurwitz class numbers

2008 ◽  
Vol 128 (6) ◽  
pp. 1847-1863 ◽  
Author(s):  
Brittany Brown ◽  
Neil J. Calkin ◽  
Timothy B. Flowers ◽  
Kevin James ◽  
Ethan Smith ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Class Numbers

Introduction to Elliptic Curves and Modular Forms

1995 ◽  
Vol 79 (484) ◽  
pp. 216
Author(s):  
John Cremona ◽  
Neal Koblitz
Keyword(s):  
Elliptic Curves ◽  
Modular Forms

SUPERSINGULAR RANK TWO DRINFEL'D MODULES AND ANALOGS OF ATKIN'S ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 05 (05) ◽  
pp. 885-895 ◽  
Author(s):  
DORIS DOBI ◽  
NICHOLAS WAGE ◽  
IRENA WANG
Keyword(s):  
Orthogonal Polynomials ◽  
Elliptic Curves ◽  
Modular Forms ◽  
Precise Relationship

The theory of elliptic curves and modular forms provides a precise relationship between the supersingular j-invariants and the congruences between modular forms. Kaneko and Zagier discuss a surprising generalization of these results in their paper on Atkin orthogonal polynomials. In this paper, we define an analog of the Atkin orthogonal polynomials for rank two Drinfel'd modules.

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