Probability and elliptic curves (I, II and III)
Document Type
Lecture
Publication Date
1-28-2014
Abstract
This expository lecture will be the (first/second/third) of a short series surveying work of Lang and Trotter from the 1970s. For an elliptic curve y2 = x3 + ax + b (with a and b integers) and a prime number p, one may consider the elliptic curve modulo p, i.e. one may consider the equation y2 congruent to x3 + ax + b modulo p. In particular, it is of wide interest to understand the number Np of solutions (x,y) modulo p to this congruence, and how this number Np varies as the prime p varies. In these lectures, we will use probabilistic notions to make very precise conjectures about some aspects of the variation of Np with p. This talk will be accessible to graduate students.
Relational Format
presentation
Recommended Citation
Jones, Nathan, "Probability and elliptic curves (I, II and III)" (2014). Algebra/Number Theory Seminar. 40.
https://egrove.olemiss.edu/math_algebra_number_theory/40
Comments
(This was a 3-part lecture series. Part I occurred on January 28, part II occurred on February 6, and part III occurred on February 13, 2014.)