15 citations · 53 across the 7 of their papers we have counts for
7 papers
Discretisation for odd quadratic twists
J. Brian Conrey, Michael O. Rubinstein, Nina C. Snaith +1
The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random…
Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions
J. Brian Conrey, Atul Pokharel, Michael O. Rubinstein +1
We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical…
Some remarks on Heegner point computations
Mark Watkins
We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Dela…
Rank distribution in a family of cubic twists
Mark Watkins
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive proportion of the even-signed cubic twists of the elliptic curve should h…
Explicit lower bounds on the modular degree of an elliptic curve
Mark Watkins
We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational ellipt…
Modular Parametrizations of Neumann-Setzer Elliptic Curves
William Stein, Mark Watkins
Suppose is a prime of the form for some integer , which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves and of prime conductor…