BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jason Bell DTSTART:20261110T140000Z DTEND:20261110T150000Z DTSTAMP:20261109T050832Z UID:CombinatoricsOnWords/144 DESCRIPTION:Title: Mahler series whose coefficient sequences are multiplicativ e\nby Jason Bell as part of One World Combinatorics on Words Seminar\n \n\nAbstract\nA recurring theme in number theory and automata theory is th at sequences exhibiting two seemingly unrelated kinds of structure are oft en highly constrained. A classical example is Cobham's theorem\, which sta tes that a sequence that is automatic with respect to two multiplicatively independent bases must be eventually periodic. Another example comes from multiplicative automatic sequences: k-automatic sequences a(n) satisfying a(mn) = a(m)a(n) whenever m and n are relatively prime. Building on earli er work of Yazdani and Coons\, Konieczny\, Lemańczyk\, and Müllner obtai ned a complete classification of such sequences. In joint work with Daniel Smertnig\, we extend this result from automatic sequences to complex powe r series satisfying Mahler functional equations. We show that if the coeff icients of a k-Mahler series are multiplicative\, then they form a k-regul ar sequence\, and we give an explicit classification of all such series. I n particular\, if k is not a prime power\, then we show that the series mu st be rational.\n LOCATION:https://researchseminars.org/talk/CombinatoricsOnWords/144/ END:VEVENT END:VCALENDAR