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SUMMARY:Kunihiro Ito (NEC Corporation/Tohoku University)
DTSTART:20201103T084000Z
DTEND:20201103T091000Z
DTSTAMP:20260423T010809Z
UID:JENTE/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/8/">On
  a multi-variable Arakawa-Kaneko zeta function for non-positive or positiv
 e indices</a>\nby Kunihiro Ito (NEC Corporation/Tohoku University) as part
  of Japan Europe Number Theory Exchange Seminar\n\n\nAbstract\nThe Arakawa
 -Kaneko zeta function (the xi function) and Kaneko-Tsumura zeta function (
 the eta function) are defined as the Mellin transformation of the generati
 ng function of multi-poly-Bernoulli numbers and notably related to multi-p
 oly-Bernoulli numbers and multiple zeta values. One striking discovery is 
 the duality of the multi-variable eta function. Specifically\, one can obt
 ain the duality formula among multi-indexed poly-Bernoulli numbers of B-ty
 pe and\, using the formula for special values of the multi-variable eta fu
 nction in terms of a linear combination of multiple zeta values\, a new fa
 mily of relations among multiple zeta values.\nIn this talk\, we introduce
  our study on the multi-variable xi function. First\, its analytic continu
 ation to an entire function. Second\, a duality formula among multi-indexe
 d poly-Bernoulli numbers of C-type which is regarded as a special case of 
 the possible duality of the multi-variable xi function. Third\, an explici
 t procedure for writing the special values of the multi-variable xi functi
 on as a linear combination of multiple zeta values.\n
LOCATION:https://researchseminars.org/talk/JENTE/8/
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