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We derive an expression for the value $ zeta_Q (3) $ of the spectral zeta function $ zeta_Q (s) $ for the non-commutative harmonic oscillator using a Gaussian hypergeometric function. In this study, t...wo sequences of rational numbers, denoted $ \tilde{J}_2 (n) $ and $ \tilde{J}_3 (n) $, which can be regarded as analogues of the $ mathnormal{Apery numbers} $, naturally arise and play a key role in obtaining the expressions for the values $ zeta_Q (2) $ and $ zeta_Q (3) $. We also show that the numbers $ \tilde{J}_2 (n) $ and $ \tilde{J}_3 (n) $ have congruence relations such as those of the Apery numbers.続きを見る
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Mendeley出力
