Perspectives on the Riemann Hypothesis

黎曼假设是纯数学中一个著名的未解决问题，可以追溯到1859年。它的动机是找到质数的精确计数，直到一个大的数量。在现代，黎曼假设被认为是数论中出现的几乎所有计数问题的基本结构的众多类似问题之一。为了促进这一问题的进展，将于2018年6月4日至7日在布里斯托尔大学举行为期三天半的会议，140名与会者将参加。会议期间将有大约15场讲座，并将安排时间讨论有前途的途径。美国的研究人员参加这次会议是很重要的；特别是最近的博士学位获得者和来自代表性不足群体的研究人员被鼓励申请参加。这个奖项将有助于支持这项特别的努力。会议网站http://heilbron.ac。我们相信黎曼假设的类似物应该适用于Selberg类中的每一个l -函数，或者等价地适用于某一类型的每一个倒丘自同构l -函数。实际上已经尝试了几十种方法。这次会议的预期结果是，将把具有相似之处的各种方法组合在一起，以便更好地评估它们的可行性。通过这种方式，重点将缩小到几个更有前途的途径。

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.