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Title :非可換調和振動子のスペクトルゼータ関数の特殊値とモジュラー形式
Title alternative :Special values of the spectral zeta function for the noncommutative harmonic oscillator and modular forms
Authors :木本, 一史
Authors alternative :Kimoto, Kazufumi
Issue Date :4-Jun-2010
Abstract :2008年度~2009年度科学研究費補助金(若手研究(B))研究成果報告書
研究概要(英文) : We have studied the spectral zeta function associated to a differential operator called the noncommutative harmonic oscillator (NCHO in short). Each special value (i.e. the values at integral points) of the spectral zeta is expressed as a sum of a Riemann zeta value and certain terms (remainder terms) involving the structure parameter of NCHO, which is thought to reflect the noncommutativity of the NCHO. These remainder terms induce higher analogue of Apery-like numbers and some variants of multiple zeta values. We found a certain structure among the generating functions of these higher Apery-like numbers, as well as calculate explicitly the multiple zeta values associated to the remainder terms.
Type Local :研究報告書
Publisher :木本一史
URI :http://hdl.handle.net/20.500.12000/18111
Appears in Collections:Research Report (Faculty of Science)

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