中科院数学与系统科学研究院

数学研究所

数论研讨班

报告人：Dr. Grimmelt L.P.（Utrecht University）

题  目：Goldbach Numbers in Short Intervals-The Bohr Set Approach

时  间：2019.09.10（星期二），10:30-11:30

地  点：数学院南楼N602室

摘  要：We believe that every even integer larger than 2 is the sum of two primes, a Goldbach number. Even though this seems out of reach with current methods, we can show that the set of exceptions to this is sparse. Famously, Montgomery and Vaughan showed that one can achieve power saving when bounding the exceptions up to some parameter X. In another direction, we can ask if something similar stays true in short intervals. In other words, for what X, H are almost all even integers between X and X+H the sum of two primes? This question has attracted the attention of different researchers and the best results are from Jia and Harman, who respectively showed that H>X^0.0648 and H>X^0.0611 are admissible.  In this talk I want to present some work in progress that applies a Bohr set Circle Method, based on Green’s transference principle, to improve the range to H>X^0.0583.