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Andrei Shubin: Prime number theorem for sums of digits in several bases

Time: Fri 2024-04-19 10.00 - 10.50

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Andrei Shubin (Vienna University of Technology)

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Abstract:

 In 1967, Gelfond established an asymptotic formula for the sum of digits of an integer \(n\) in base \(q\) in arithmetic progressions. He conjectured similar formulas for the sums of digits of primes and integer polynomials. The case of primes was completely resolved in the famous work of Mauduit and Rivat (2010). Later, Drmota, Mauduit, and Rivat (2020) extended this result for sums of digits of primes in two different bases simultaneously. In this talk, we will describe the proof for any number of bases. We will also discuss the connection of these results to ergodic theory and automata.

This is a joint work in progress with Clemens Müllner.