most citedRank distribution in a family of cubic twists

15 citations · 53 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT20056 cited

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…

math.NT200511 cited

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…

math.NT200510 cited

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…

math.NT200415 cited

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…

math.NT20044 cited

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…

math.NT20044 cited

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…