A first course in sieve methods

Fall 2022 ＆ Spring 2023, Jinan

Organizers:

Shenghao Hua, Bingrong Huang, Zhiwei Wang.

Time and Place: 

Fall 2022: Thursday 14:00-16:00, Zhixin Building B1044.

Spring 2023: TBA

Prerequisites:

Elementary Number Theory.

Synopsis:

This is a reading seminar. We plan to read Friedlander and Iwaniec’s sieve method book Opera de cribro, and some applications of sieve methods and large sieve methods, such as Goldbach’s Conjecture, Twin Prime Conjecture, and so on. This is also a joint course with Professor Zhiwei Wang’s Advanced Analytic Number Theory course in Fall 2022.

Reference:

[Chen66]. Chen Jing-run. On the representation of a large even integer as the sum of a prime and the product of at most two primes. Kexue Tongbao 17 (1966), 385–386.

[FI10]. Friedlander, John; Iwaniec, Henryk. Opera de cribro. American Mathematical Society Colloquium Publications, 57. American Mathematical Society, Providence, RI, 2010.

[FI09]. Friedlander, John; Iwaniec, Henryk. What is … the parity phenomenon? Notices Amer. Math. Soc. 56 (2009), no. 7, 817–818.

[HR74].Halberstam, H.; Richert, H.-E. Sieve methods. London Mathematical Society Monographs, No. 4. Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1974.

[Maynard15]. Maynard, James. Small gaps between primes. Ann. of Math. (2) 181 (2015), no. 1, 383–413.

[Zhang14]. Zhang, Yitang. Bounded gaps between primes. Ann. of Math. (2) 179 (2014), no. 3, 1121–1174.