14 citations · 39 across the 5 of their papers we have counts for
7 papers
On the Lang-Trotter conjecture for two elliptic curves
Amir Akbary, James Parks
Following Lang and Trotter we describe a probabilistic model that predicts the distribution of primes with given Frobenius traces at for two fixed elliptic curves over $\ma…
Low-lying zeros of quadratic Dirichlet -functions: A transition in the Ratios Conjecture
Daniel Fiorilli, James Parks, Anders Södergren
We study the -level density of low-lying zeros of quadratic Dirichlet -functions by applying the -functions Ratios Conjecture. We observe a transition in the main term as…
Low-lying zeros of quadratic Dirichlet -functions: Lower order terms for extended support
Daniel Fiorilli, James Parks, Anders Södergren
We study the -level density of low-lying zeros of Dirichlet -functions attached to real primitive characters of conductor at most . Under the Generalized Riemann Hypothesi…
An asymptotic for the average number of amicable pairs for elliptic curves
James Parks
Amicable pairs for a fixed elliptic curve defined over were first considered by Silverman and Stange where they conjectured an order of magnitude for the function that…
Low-lying zeros of elliptic curve L-functions: Beyond the ratios conjecture
Daniel Fiorilli, James Parks, Anders Södergren
We study the low-lying zeros of L-functions attached to quadratic twists of a given elliptic curve E defined over . We are primarily interested in the family of all twis…
Amicable pairs and aliquot cycles on average
James Parks
Silverman and Stange defined the notion of an aliquot cycle of length for a fixed elliptic curve , and conjectured an order of magnitude for the function that cou…
One-level density of families of elliptic curves and the Ratios Conjectures
Chantal David, Duc Khiem Huynh, James Parks
Using the ratios conjectures as introduced by Conrey, Farmer and Zirnbauer, we obtain closed formulas for the one-level density for two families of L-functions attached to elliptic…