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SUMMARY:Li Lai (Tsinghua University)
DTSTART:20230405T073000Z
DTEND:20230405T083000Z
DTSTAMP:20260423T035817Z
UID:PekiNT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PekiNT/2/">O
 n the irrationality of certain 2-adic zeta values</a>\nby Li Lai (Tsinghua
  University) as part of PKU/BICMR Number Theory Seminar\n\nLecture held in
  Room 77201\, BICMR.\n\nAbstract\nLet $\\zeta_2(\\cdot)$ be the Kubota-Leo
 poldt $2$-adic zeta function. We prove that\, for every nonnegative intege
 r $s$\, there exists an odd integer $j$ in the interval $[s+3\,3s+5]$ such
  that $\\zeta_2(j)$ is irrational. In particular\, at least one of $\\zeta
 _2(7)\,\\zeta_2(9)\,\\zeta_2(11)\,\\zeta_2(13)$ is irrational.\n\nOur appr
 oach is inspired by the recent work of Sprang. We construct explicit ratio
 nal functions. The Volkenborn integrals of the (higher order) derivatives 
 of these rational functions produce good linear combinations of $1$ and $2
 $-adic Hurwitz zeta values. The most difficult step is to prove that certa
 in Volkenborn integrals are nonzero\, which is resolved by careful manipul
 ation of the binomial coefficients.\n\nZoom number: 743 736 2326\n\nPasswo
 rd: 013049\n
LOCATION:https://researchseminars.org/talk/PekiNT/2/
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