学术报告

Voronoi Formulas and its Generalizations

阅读次数:1122

题目:Voronoi Formulas and its Generalizations

报告人:周帆 博士(University of Maine)

地点:致远楼103室

时间:2018年6月29日 10:00—11:00

摘要:Voronoi formulas are Poisson-style summation formulas for automorphic forms (on GL(n)). They have been powerful tools in analytic number theory for a long time (with applications to the divisor problem, the circle problem, subconvexity of L-functions, etc). Firstly, we present a Voronoi formula for coefficients of a large class of L-functions, in the style of the classical converse theorem of Andre Weil. Our formula applies to full-level cusp forms, Rankin-Selberg convolutions, and isobaric sums. Secondly, we present the balanced Voronoi formula, with its both sides twisted by hyper-Kloosterman sums. Lastly, we will discuss how the formula will be generlized when the automorphic form has ramifications.
报告人简介:周帆,美国缅因大学助理教授。2008年本科毕业于北京大学数学科学学院,2013年博士毕业于美国哥伦比亚大学,师从Dorian Goldfeld。主要研究方向为自守形式和L-函数;在American Journal of Mathematics、 Algebra & Number Theory、Journal of Number Theory等高水平学术期刊上发表多篇论文。

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