BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Akash Singha Roy (University of Georgia) DTSTART:20250520T190000Z DTEND:20250520T192500Z DTSTAMP:20260423T010421Z UID:CANT2025/22 DESCRIPTION:Title: Joint distribution in residue classes of families of multiplicative func tions\nby Akash Singha Roy (University of Georgia) as part of Combinat orial and additive number theory (CANT 2025)\n\nLecture held in CUNY Gradu ate Center - Science Center (4th floor).\n\nAbstract\nThe distribution of values of arithmetic functions in residue classes has been a problem of gr eat interest in elementary\, analytic\, and combinatorial number theory. I n work studying this problem for large classes of multiplicative functions \, Narkiewicz obtained general criteria deciding when a family of such fun ctions is jointly uniformly distributed among the coprime residue classes to a fixed modulus. Using these criteria\, he along with \\' Sliwa\, Rayne r\, Dobrowolski\, Fomenko\, and others\, gave explicit results on the dist ribution of interesting multiplicative functions and their families in cop rime residue classes.\n\nIn this talk\, we shall give best possible extens ions of Narkiewicz's criteria (and hence also of the other aforementioned results) to moduli that are allowed to vary in a wide range. This is motiv ated by the celebrated Siegel-Walfisz theorem on the distribution of prime s in arithmetic progressions\, and our results happen to be some of the be st possible qualitative analogues of the Siegel-Walfisz theorem for the cl asses of multiplicative functions considered by Narkiewicz and others. Our arguments blend ideas from multiple subfields of number theory\, as well as from linear algebra over rings\, commutative algebra\, and arithmetic a nd algebraic geometry. This talk is partly based on joint work with Paul P ollack.\n LOCATION:https://researchseminars.org/talk/CANT2025/22/ END:VEVENT END:VCALENDAR