BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Drmota (TU Wien) DTSTART:20210330T123000Z DTEND:20210330T133000Z DTSTAMP:20260423T021222Z UID:OWNS/39 DESCRIPTION:Title: (L ogarithmic) Densities for Automatic Sequences along Primes and Squares \nby Michael Drmota (TU Wien) as part of One World Numeration seminar\n\n\ nAbstract\nIt is well known that the every letter $\\alpha$ of an automati c sequence $a(n)$ has\na logarithmic density -- and it can be decided when this logarithmic density is actually a density.\nFor example\, the letter s $0$ and $1$ of the Thue-Morse sequences $t(n)$ have both frequences $1/2 $.\n[The Thue-Morse sequence is the binary sum-of-digits functions modulo 2.]\n\nThe purpose of this talk is to present a corresponding result for s ubsequences of general\nautomatic sequences along primes and squares. This is a far reaching generalization of two breakthrough\nresults of Mauduit and Rivat from 2009 and 2010\, where they solved two conjectures by Gelfon d\non the densities of $0$ and $1$ of $t(p_n)$ and $t(n^2)$ (where $p_n$ d enotes the sequence of primes).\n\nMore technically\, one has to develop a method to transfer density results for primitive automatic\nsequences to logarithmic-density results for general automatic sequences. Then as an ap plication\none can deduce that the logarithmic densities of any automatic sequence along squares\n$(n^2)_{n\\geq 0}$ and primes $(p_n)_{n\\geq 1}$ e xist and are computable.\nFurthermore\, if densities exist then they are ( usually) rational.\n LOCATION:https://researchseminars.org/talk/OWNS/39/ END:VEVENT END:VCALENDAR