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Explore Ram Murty's lecture from Queen's University on Artin's Conjectures in this 51-minute CRM-Fields-PIMS Prize Lecture. Delve into Emil Artin's groundbreaking work from the 1920s, when he defined non-abelian L-series and formulated his holomorphy conjecture, proposing that these L-series extend holomorphically to the entire complex plane (except for a possible pole at s=1). Learn how Artin demonstrated these L-series could solve classical problems in analytic number theory, including his famous primitive root conjecture. Though these conjectures remain unsolved after more than a century, discover the significant progress made in understanding them as Professor Murty surveys key developments in this important area of mathematics.
