APERY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS

スポンサーリンク

概要

• 論文の詳細を見る

• 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, two 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.

著者

• Wakayama Masato

  Faculty Of Mathematics Kyushu University

• KIMOTO Kazufumi

  Department of Mathematical Science University of the Ryukyus

関連論文

• APERY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS
• PERIOD DEFORMATIONS AND RAABE'S FORMULAS FOR GENERALIZED GAMMA AND SINE FUNCTIONS
• Remarks on Shintani's zeta function
• Splitting density for lifting about discrete groups
• Regularizations and finite ladders in multiple trigonometry
• EXTREMAL VALUES OF DOUBLE AND TRIPLE TRIGONOMETRIC FUNCTIONS
• A VARIATION OF EULER'S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION
• ZETA REGULARIZATIONS AND $q $-ANALOGUE OF RING SINE FUNCTIONS

スポンサーリンク