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Based on the method of reduction to absurdity, I convert the Fermat Equation into an open curve, which is inequivalent to the elliptic curve Professor Wiles deduced through “making out cubic curve”.
Based on the method of reduction to absurdity, I convert the Fermat Equation into an open curve, which is inequivalent to the elliptic curve Professor Wiles deduced through “making out cubic curve”.
A Random Matrix Model for Elliptic Curve $L$-Functions of Finite Conductor
Elliptic Curves Low Lying Zeros n-Level Statistics Random Matrix Theory Jacobi Ensembles Characteristic Polynomial
2011/9/19
Abstract: We propose a random matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of their critical zeros away from the center of the critical strip was observed b...
Constructing elliptic curve isogenies in quantum subexponential time
Constructing elliptic curve isogenies quantum subexponential time
2011/3/3
Given two elliptic curves over a finite field having the same cardinality and endomorphism
ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to ...
An elliptic curve test of the L-Functions Ratios Conjecture
An elliptic curve test the L-Functions Ratios Conjecture
2010/11/19
We compare the L-Function Ratios Conjecture's prediction with number theory for the family of quadratic twists of a fixed elliptic curve with prime conductor, and show agreement in the 1-level densit...
On the Mordell--Weil group of the elliptic curve y^2=x^3+n
On the Mordell--Weil group the elliptic curve y^2=x^3+n
2010/11/11
We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We show that the points are independent in certain ...
On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve
Ranks of the 2-Selmer Groups of Twists Given Elliptic Curve
2010/12/1
On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve.
The main result of this paper is the proof of the "transversal part" of the homological mirror symmetry conjecture for an elliptic curve which states an equivalence of two $A_{\infty}$-structures on ...
The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
elliptic curve S-duality theory Eisenstein series Kac-Moody groups
2010/10/29
We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for Kac-Moody groups. For a pair consisting of a surfa...