Perspectives on the Riemann Hypothesis

点击翻译按钮获取中文摘要

The Riemann Hypothesis is a celebrated unsolved problem in pure mathematics that dates back to 1859. Its motivation is to find a precise count for the number of prime numbers up to a large quantity. In modern times the Riemann Hypothesis is recognized as one of a host of similar problems about the underlying structure of nearly every counting problem that arises in number theory. In order to stimulate progress on this problem a three-and-a-half day conference will be held at the University of Bristol June 4 - 7, 2018 for up to 140 participants. There will be about 15 lectures during the meeting and there will be time scheduled for discussion of promising avenues. It is important that U.S. based researchers attend this meeting; especially recent PhD recipients and researchers from under-represented groups are encouraged to apply to attend. This award will help support that particular effort. The website for the conference ishttps://heilbronn.ac.uk/2017/08/08/perspectives-on-the-riemann-hypothesis/It is believed that the analogue of the Riemann Hypothesis should hold for every L-function in the Selberg Class, or equivalently for every cuspidal automorphic L-function of a certain type. There are literally dozens of approaches that have been tried. An expected outcome of this meeting is that various approaches with similarities will be grouped together in order to better assess their viability. In this way the focus will be narrowed to a few of the more promising avenues.