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SUMMARY:Stefano Marmi (Scuola Normale Superiore)
DTSTART:20231031T130000Z
DTEND:20231031T140000Z
DTSTAMP:20260423T021417Z
UID:OWNS/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/120/">C
 omplexified continued fractions and complex Brjuno and Wilton functions</a
 >\nby Stefano Marmi (Scuola Normale Superiore) as part of One World Numera
 tion seminar\n\n\nAbstract\nWe study functions related to the classical Br
 juno function\, namely k-Brjuno functions and the Wilton function. Both ap
 pear in the study of boundary regularity properties of (quasi) modular for
 ms and their integrals. We then complexify the functional equations which 
 they fulfill and we construct analytic extensions of the k-Brjuno and Wilt
 on functions to the upper half-plane. We study their boundary behaviour us
 ing an extension of the continued fraction algorithm to the complex plane.
  We also prove that the harmonic conjugate of the real k-Brjuno function i
 s continuous at all irrational numbers and has a decreasing jump of π/qk 
 at rational points p/q. This is based on joint work with S. B. Lee\, I. Pe
 trykiewicz and T. I. Schindler\, the paper is available (open source) at t
 his link: https://link.springer.com/article/10.1007/s00010-023-00967-w\n
LOCATION:https://researchseminars.org/talk/OWNS/120/
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