While questions about prime numbers are ancient, many such questions remained unresolved well into the 20th century, with an exponential acceleration of techniques and results happening in the past few decades. Analytic number theory focuses on such questions through the lens of L-functions, which are generating series that encode arithmetic information and  induce connections with a host of other mathematical fields, such as algebraic number theory, harmonic analysis, Diophantine approximation, probability, representation theory, and computational number theory. The many important results established in analytic number theory throughout the last decade include influential work on bounded gaps between primes (Zhang, Maynard, Tao, and Polymath), multiplicative functions in short intervals (Matomäki–Radziwiłł), and the resolution of the Erdős discrepancy conjecture (Tao). The field has also witnessed an influx of work on the Chowla and Sarnak conjectures which connect number theory to ergodic theory and combinatorics. In addition, random matrix theory has played a instrumental role in informing research in analytic number theory, after Keating and Snaith used it to derive now widely believed conjectures for moments of L-functions that had mystified the number theory community for decades. 

This PIMS-CRG in analytic number theory is timely and relevant due to the surge of activity in the last decade in fields related to L-functions. Over the past five years, an exciting new generation of researchers has been hired in these fields in both BC and Alberta, including Fiori, Hamieh, Nguyen, Patnaik, Tran, and Xiao. This CRG is a proposal to build upon this momentum to focus and strengthen the current local network of number theorists at UNBC, UBC, SFU, and the universities of Alberta, Calgary, and Lethbridge, expanding our region's role in the international research network. 

Our ambitious goals include tackling a variety of central problems in analytic number theory and elevating a new generation of experts that is more representative of our diverse society. 

The three highlight events of our CRG will be two workshops and a summer school, all of which incorporate EDI content into their schedules; of special note is the summer school "Inclusive Paths in Explicit Number Theory", where the junior participants will be generating research publications in structured groups. Scientific plans also include three joint PIMS-network graduate courses, an online CRG seminar, focused research groups with Distinguished Research Visitors, and two postdoctoral fellows. 

These CRG leaders all have been actively very involved in organizing various events which have strengthened the number theory community in British Columbia and Alberta and built a supportive network for students and postdocs.

Martin and Ng have been long term seminar organizers in their respective institutions (UBC Number Theory Seminars 2001-2017 and PIMS-Lethbridge Number Theory and Combinatorics since 2011). Hamieh and Kadiri respectively started and organized the PIMS-UNBC Distinguished Colloquium Series since 2018 and the PIMS-Lethbridge Distinguished Speaker series since 2013. All CRG leaders also all have a history of organizing PIMS-sponsored research events and educational activities, such as the annual 2-day BIRS workshop Alberta Number Theory Days (co-founded in 2008 by Kadiri and Ng, co-organized 7 times by Hamieh, Kadiri, and/or Ng since then) and the recent summer school Inclusive Paths in Number Theory (Kadiri in 2021). In addition, Ng has been the chair of the Digital Collaboration Committee planning the PIMS Network Digital Courses since 2020. 

They have also co-organized large international conferences such as the L-functions and their Applications to Number Theory (Martin in Calgary 2006), and the biennial Canadian Number Theory Association meetings (Martin in Vancouver 2006, Kadiri and Ng in Lethbridge 2012). In addition, they have organized several special sessions at CMS and AMS meetings (Hamieh for CMS 2018 and JMM 2022; Hamieh, Kadiri, Martin and Ng for CMS 2018; Martin for JMM 2008 and MCA 2017). 

In all past activities, CRG leaders have all been committed to upholding EDI principles and giving special attention to female representation and to student participation. The last generation of female number theorists have benefited from accelerator programs such as the Women In Numbers workshops and network. This team is committed to offering a productive and inclusive space to facilitate exchange of ideas, foster collaboration among participants, and train junior researchers and to boost representation and participation of mathematicians from equity-deserving groups.