Colloquium / Seminars
Topic：Cyclicity of CM Elliptic Curves Modulo p in Short Intervals
Speaker：Dr. Peng-Jie Wong
Date time：Mar. 9, 2021 14:00 - 15:00
Tea Party：Mar. 9, 2021 13:30 (SA205)
Abstract：Abstract. Let E be a CM elliptic curve defined over the rational numbers. In light of the Lang-Trotter conjecture, there is a question asking for an asymptotic formula for the number of primes p < x for which the reduction modulo p of E is cyclic. This question can be seen as an "elliptic" analogue of the prime number theorem and has been studied by many mathematicians.
In this talk, we will start by reviewing the prime number theorem and some properties of elliptic curves. After reviewing, we will discuss the previous work and a short interval variant of the above-mentioned "cyclicity problem", which presents a generalisation of Huxley's work on the prime number theorem in short intervals. If time allows, we will further discuss some ingredients of the proof.