Special values of the spectral zeta function for the noncommutative harmonic oscillator and modular forms
| Project/Area Number |
20740021
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
KIMOTO Kazufumi University of the Ryukyus, 理学部, 助教 (10372806)
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| Project Period (FY) |
2008 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 非可換調和振動子 / スペクトルゼータ関数 / 特殊値 / モジュラー形式 / スペクトルゼー関数 / パラメタ変形 / 多重ゼータ値 |
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| Research Abstract |
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.
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Report
(3 results)
Research Products
(12 results)
