11 citations
6 papers
A Single Differential Equation Description of Membrane Properties Underlying the Action Potential and the Axon Electric Field
Robert F. Melendy, Ph. D
In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation i…
On Surfaces that are Intrinsically Surfaces of Revolution
Daniel Freese, Matthias Weber
We consider surfaces in Euclidean space parametrized on an annular domain such that the first fundamental form and the principal curvatures are rotationally invariant, and the prin…
Sums of Euler products and statistics of elliptic curves
Chantal David, Dimitris Koukoulopoulos, Ethan Smith
We present several results related to statistics for elliptic curves over a finite field as corollaries of a general theorem about averages of Euler products that we…
The frequency of elliptic curve groups over prime finite fields
Vorrapan Chandee, Chantal David, Dimitris Koukoulopoulos +1
Letting vary over all primes and vary over all elliptic curves over the finite field , we study the frequency to which a given group arises as a group of…
Group structures of elliptic curves over finite fields
Vorrapan Chandee, Chantal David, Dimitris Koukoulopoulos +1
It is well-known that if is an elliptic curve over the finite field , then for some pos…
Averages of the number of points on elliptic curves
Greg Martin, Paul Pollack, Ethan Smith
If is an elliptic curve defined over and is a prime of good reduction for , let denote the set of points on the reduced curve modulo . De…