Add to ORKGSuppose you are given an algebraic curve C defined over the rational number field, defined, let us say, as the locus of zeroes of a polynomial in two variables, f(x, y) with rational coefficients. Suppose you are told that C has at least one rational point, i.e., that there is a pair of rational numbers (a, b) such tha
Abstract. We generalize a construction of families of moderate rank elliptic curves over Q to number...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
Let E be an elliptic curve over Q. Then, we show that the average analytic rank of E over cyclic ext...
Rational points of elliptic curves are gems of the arithmetic theory. One mesure of the size of the ...
The parity of the analytic rank of an elliptic curve is given by the root number in the functional e...
All the results in this paper are conditional on the Riemann Hypothesis for the L-functions of ellip...
We show that the average and typical ranks in a certain parametric family of elliptic curves describ...
In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic c...
All the results in this paper are conditional on the Riemann hypothesis for the L-functions of ellip...
AbstractThis paper studies the family of elliptic curves Em: X3 + Y3 = m where m is a cubefree integ...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
Abstract. We generalize a construction of families of moderate rank elliptic curves over Q to number...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
Let E be an elliptic curve over Q. Then, we show that the average analytic rank of E over cyclic ext...
Rational points of elliptic curves are gems of the arithmetic theory. One mesure of the size of the ...
The parity of the analytic rank of an elliptic curve is given by the root number in the functional e...
All the results in this paper are conditional on the Riemann Hypothesis for the L-functions of ellip...
We show that the average and typical ranks in a certain parametric family of elliptic curves describ...
In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic c...
All the results in this paper are conditional on the Riemann hypothesis for the L-functions of ellip...
AbstractThis paper studies the family of elliptic curves Em: X3 + Y3 = m where m is a cubefree integ...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
Abstract. We generalize a construction of families of moderate rank elliptic curves over Q to number...
We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was re...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...