BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sacha Mangerel (University of Montreal) DTSTART:20210217T171500Z DTEND:20210217T181500Z DTSTAMP:20260423T022810Z UID:IML_NT/7 DESCRIPTION:Title: D iscrepancy Problems for Multiplicative Functions over F_q[t]\nby Sacha Mangerel (University of Montreal) as part of IML Number Theory semester ( spring 2021)\n\n\nAbstract\nAn equivalent form of the famous Erdos Discrep ancy Problem\, proved by\nTao building on the work of the Polymath5 projec t\, states that any\ncompletely multiplicative function taking values on t he unit circle has\nunbounded partial sums. It was observed in the course of the Polymath5\nproject that the same is not true if one considers the m ost natural\ntranslation of this problem to the ring F_q[t] of polynomials over a\nfinite field.\n\nWe will discuss recent joint work with O. Klurma n and J. Teräväinen\ndemonstrating that the function field discrepancy p roblem depends\nheavily on the way the elements of the sums are ordered\, in contrast to\nthe integer setting. In particular\, we will introduce thr ee different\nnotions of discrepancy\, and discuss the problem of classify ing those\ncompletely multiplicative functions that have uniformly bounded partial\nsums with respect to each of these notions. We will also addres s the\nproblem of bounding the minimal rate of growth of unbounded partial \nsums\, which is the subject of some speculation in the integer setting.\ n LOCATION:https://researchseminars.org/talk/IML_NT/7/ END:VEVENT END:VCALENDAR