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NCTS Seminar on Number Theory
10:30 - 11:30, March 8, 2019 (Friday)
R201, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 201室)
Deligne Family for Euler Sums of Depth Two
Nobuo Sato (Kyushu University)


In his work on motivic multiple L-values, Deligne gave an algebraic generator for the space of motivic Euler sums. Afterwards, Glanois revisited Deligne's work and gave a Q-basis for the space of motivic Euler sums using a similar construction as Deline's, which she called "Deligne family". Their proof of Deligne family being a basis makes use of the coproduct structure equipped in the space of motivic Euler sums, which does not provide a way to compute the expression (coefficients) of a given Euler sum by that basis. In this talk I will first introduce Deligne family with slight modification, and give an explicit reduction procedure by linear relation to express Euler sums of depth two by our modified Deligne family. As a natural consequence of my reduction algorithm, we find that the modified Deligne family in fact gives a Z2-basis rather than just a Q-basis. This is an on-going joint research work with Minoru Hirose at Kyushu University.


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