报告人:
Sinai Robins 【University of Sao Paulo】
报告人单位:
时间:
2019-01-29 16:00-17:00
地点:
卫津路校区6号楼108教
开始时间:
2019-01-29 16:00-17:00
报告人简介:
年:
日月:
报告人简介
University of Sao Paulo教授
报告内容介绍
In 1951 Erdos proposed the following problem: Suppose we tile the integers
Z with any finite, disjoint union of arithmetic progressions. Then it must be true that at least two of these progressions are translates of each other. In 2012, we extended this problem to the tiling of with translated sublattices, where the desired conclusion is still open for
d=2. In 2018, we discovered a new analytic formula, which uses some analytic number theory, and which we call a Lipschitz summation formula for cones. We then apply this Cone Lipschitz summation formula to this problem to get a new formulation in terms of certain group characters for the relevant finite abelian groups that come up naturally when one considers such a decomposition of the integer lattice into translated sublattices.