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SUMMARY:Nikita Shulga (La Trobe University)
DTSTART:20240326T130000Z
DTEND:20240326T140000Z
DTSTAMP:20260423T053132Z
UID:OWNS/128
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/128/">R
 adical bound for Zaremba’s conjecture</a>\nby Nikita Shulga (La Trobe Un
 iversity) as part of One World Numeration seminar\n\n\nAbstract\nZaremba's
  conjecture states that for each positive integer $q$\, there exists a cop
 rime integer $a$\, smaller than $q$\, such that partial quotients in the c
 ontinued fraction expansion of $a/q$ are bounded by some absolute constant
 . Despite major breakthroughs in the recent years\, the conjecture is stil
 l open. In this talk I will discuss a new result towards Zaremba's conject
 ure\, proving that for each denominator\, one can find a numerator\, such 
 that partial quotients are bounded by the radical of the denominator\, i.e
 . the product of distinct prime factors. This generalizes the result by Ni
 ederreiter and improves upon some results of Moshchevitin-Murphy-Shkredov.
 \n
LOCATION:https://researchseminars.org/talk/OWNS/128/
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