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SUMMARY:Eda Cesaratto (Univ. Nac. de Gral. Sarmiento & CONICET)
DTSTART:20220412T123000Z
DTEND:20220412T133000Z
DTSTAMP:20260423T052932Z
UID:OWNS/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/82/">Lo
 chs-type theorems beyond positive entropy</a>\nby Eda Cesaratto (Univ. Nac
 . de Gral. Sarmiento & CONICET) as part of One World Numeration seminar\n\
 n\nAbstract\nLochs' theorem and its generalizations are conversion theorem
 s that relate the number of digits determined in one expansion of a real n
 umber as a function of the number of digits given in some other expansion.
  In its original version\, Lochs' theorem related decimal expansions with 
 continued fraction expansions. Such conversion results can also be stated 
 for sequences of interval partitions under suitable assumptions\, with res
 ults holding almost everywhere\, or in measure\, involving the entropy. Th
 is is the viewpoint we develop here. In order to deal with sequences of pa
 rtitions beyond positive entropy\, this paper introduces the notion of log
 -balanced sequences of partitions\, together with their weight functions. 
 These are sequences of interval partitions such that the logarithms of the
  measures of their intervals at each depth are roughly the same. We then s
 tate Lochs-type theorems which work even in the case of zero entropy\, in 
 particular for several important log-balanced sequences of partitions of a
  number-theoretic nature. \n\nThis is joint work with Valérie Berthé (IR
 IF)\, Pablo Rotondo (U. Gustave Eiffel) and Martín Safe (Univ. Nac. del S
 ur & CONICET\, Argentina).\n
LOCATION:https://researchseminars.org/talk/OWNS/82/
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