演講公告

演講主題：Cyclicity of CM Elliptic Curves Modulo p in Short Intervals
主講人：Peng-Jie Wong 博士 (NCTS)
演講日期：2021年3月9日(二)14:00 –15:00
演講地點：(光復校區) 科學一館223室
茶會時間：當天下午13:30 (科學一館205室)
摘要內容：
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.
相關檔案：Talk_1100309.pdf

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