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タイトル	Non-commutative factorizations and multiple zeta values in positive characteristic
開催日時	2025年2月25日（火） 16:30 ～ 17:30
主催者
講演者	Federico Pellarin氏 (Sapienza University of Rome, Italy)
場所	慶應義塾大学理工学部（矢上キャンパス）14棟631室 *対面のみの開催となります. *講演後にPellarinさんを囲んだ食事会を行う予定です. 参加希望の方は, 2/10までにdainobu@keio.jp(臺信）へご連絡ください.
内容	The classical factorization of the sine function can be used to prove Euler’s formula that \zeta(n) is proportional to \pi^n with a rational factor of proportionality if 2 divides n, as well as similar other properties for multiple zeta values of a certain type. In 1935 Carlitz introduced his global function field variant of zeta values and proved analogue statements by constructing one of the simplest Drinfeld modules, Carlitz’s module, and inaugurating a new area of research. Later in 2004, Thakur also introduced multiple zeta values in this setting, generalizing Carlitz’s constructions. In this talk we review a joint work with Nathan Green where we attach certain sine functions to tensor powers of Carlitz’s module. While it seems difficult to construct explicit factorizations of such sine functions in the way Euler does for the classical sine function, it is instead possible to view our ``higher sine functions’’ as elements of a non-commutative algebra of operators, where they can be factorized in a simple way. This process generates non-trivial relations among function field analogues of Thakur multiple zeta values.
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