ゼータ対応の数理
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| Published in | 応用数理 Vol. 34; no. 4; pp. 316 - 328 |
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| Format | Journal Article |
| Language | Japanese |
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一般社団法人 日本応用数理学会
25.12.2024
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| ISSN | 2432-1982 |
| DOI | 10.11540/bjsiam.34.4_316 |
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| Author | 今野, 紀雄 |
|---|---|
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| Copyright | 2024 日本応用数理学会 |
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| DOI | 10.11540/bjsiam.34.4_316 |
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| EndPage | 328 |
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| PublicationTitle | 応用数理 |
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| Publisher | 一般社団法人 日本応用数理学会 |
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| References | [16] [第五作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. CTM/Zeta Correspondence. Quantum Studies: Mathematics and Foundations, Vol. 9, pp. 165–173, 2022. [10] [第九作品：ゼータ対応] Y. Ide, T. Komatsu, N. Konno, and I. Sato. Metzler/Zeta Correspondence. Discrete Mathematics, Vol. 346, 113418, 2023. [35] 黒川信重． 絶対数学原論． 現代数学社，京都， 2016. [15] [第四作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Vertex-Face/Zeta Correspondence. Journal of Algebraic Combinatorics, Vol. 56, pp. 527–545, 2022. [36] 町田拓也． 図で解る量子ウォーク入門． 森北出版，東京， 2015. [4] S. Attal, F. Petruccione, and I. Sinayskiy. Open quantum walks on graphs. Physics Letters A, Vol. 376, pp. 1545–1548, 2012. [23] 今野紀雄． 無限粒子系の科学． 講談社，東京， 2008. [18] [第十二作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Alternating Walk/Zeta Correspondence. arXiv, arXiv:2302.09583, 2023. [45] 竹居正登． 入門 確率過程． 森北出版，東京， 2020. [37] 町田拓也． 量子ウォーク―基礎と数理―. 裳華房，東京， 2018. [41] R. Portugal. Quantum Walks and Search Algorithms (2nd edition). Springer, New York, 2018. [44] F. Spitzer. Principles of Random Walk (2nd edition). Springer, New York, 1976. [9] R. Durrett. Lecture Notes on Particle Systems and Percolation. Wadsworth, Inc., California, 1988. [40] J. R. Norris. Markov Chains. Cambridge University Press, Cambridge, 1997. [22] 今野紀雄． 量子ウォークの数理． 産業図書，東京， 2008. [33] [第六作品：ゼータ対応] N. Konno, and S. Tamura. Walk/Zeta Correspondence for quantum and correlated random walks. Yokohama Mathematical Journal, Vol. 67, pp. 125–152, 2021. [1] J. Akahori, N. Konno, and I. Sato. Absolute Zeta functions for Zeta functions of quantum cellular automata. Quantum Information and Computation, Vol. 23, pp. 1261–1274, 2023. [6] G. Chinta, J. Jorgenson, and A. Karlsson. Heat kernels on regular graphs and generalized Ihara zeta function formulas. Monatshefte fur Mathematik, Vol. 178, pp. 171–190, 2015. [26] 今野紀雄． 量子ウォークによる時系列解析． 日本評論社，東京， 2020. [20] [第七作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and S. Tamura. A generalized Grover/Zeta Correspondence. arXiv, arXiv:2201.03973, 2022. [46] S. E. Venegas-Andraca. Quantum walks: A comprehensive review. Quantum Information Processing, Vol. 11, pp. 1015–1106, 2012. [42] P. Ren, T. Aleksic, D. Emms, R. C. Wilson, and E. R. Hancock. Quantum walks, Ihara zeta functions and cospectrality in regular graphs. Quantum Information Processing, Vol. 10, pp. 405–417, 2011. [11] [第十作品：ゼータ対応] C. Kiumi, N. Konno, and Y. Oshima. IPS/Zeta correspondence for the Domany–Kinzel model. Interdisciplinary Information Sciences (in press), arXiv, arXiv:2206.03188, 2022. [27] 今野紀雄． 量子探索―量子ウォークが拓く最先端アルゴリズム―． 近代科学社，東京， 2021. [29] 今野紀雄． 量子ウォークからゼータ対応へ―ゼータ関数を通して眺める数理モデル―． 日本評論社，東京， 2022. [2] 青山崇洋． 多重ゼータ関数と高次元ランダムウォーク． 応用数理, Vol. 33, No. 2, pp. 62–71, 2023. [38] K. Manouchehri, and J. Wang. Physical Implementation of Quantum Walks. Springer, New York, 2014. [24] N. Konno. Quantum walks. In Quantum Potential Theory (edited by U. Franz and M. Schurmann), Lecture Notes in Mathematics, Vol. 1954, pp. 309–452, Springer-Verlag, Heidelberg, 2008. [8] E. Domany, and W. Kinzel. Equivalence of cellular automata to Ising models and directed percolation. Physical Review Letters, Vol. 53, pp. 311–314, 1984. [32] N. Konno, and I. Sato. On the relation between quantum walks and zeta functions. Quantum Information Processing, Vol. 11, pp. 341–349, 2012. [17] [第二作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Walk/Zeta Correspondence. Journal of Statistical Physics, Vol. 190, 36, 2023. [43] R. B．シナジ． マルコフ連鎖から格子確率モデルへ． 丸善出版，東京， 2012. [21] [第八作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and S. Tamura. Mahler/Zeta Correspondence. Quantum Information Processing, Vol. 21, 298, 2022. [14] [第三作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. IPS/Zeta Correspondence. Quantum Information and Computation, Vol. 22, pp. 251–269, 2022. [3] S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy. Open quantum random walks. Journal of Statistical Physics, Vol. 147, pp. 832–852, 2012. [28] N. Konno. An analogue of the Riemann Hypothesis via quantum walks. Quantum Studies: Mathematics and Foundations, Vol. 9, pp. 367–379, 2022. [13] [第一作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Grover/Zeta Correspondence based on the Konno-Sato theorem. Quantum Information Processing, Vol. 20, 268, 2021. [39] J. McKee, and C. Smyth. Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity. Springer, Cham, 2021. [34] 黒川信重． 絶対ゼータ関数論． 岩波書店，東京， 2016. [25] 今野紀雄． 量子ウォーク． 森北出版，東京， 2014. [12] [第零作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice. Yokohama Mathematical Journal, Vol. 67, pp. 115–123, 2021. [7] B. Clair. The Ihara zeta function of the infinite grid. Electronic Journal of Combinatorics, Vol. 21, Paper 2.16, 2014. [31] 今野紀雄・井手勇介（共編著）． 量子ウォークの新展開． 培風館，東京， 2019. [30] N. Konno. On the relation between quantum walks and absolute zeta functions. Quantum Studies: Mathematics and Foundations, Vol. 11, pp. 147–157, 2024. [5] F. Brunault, and W. Zudilin. Many Variations of Mahler Measures: A Lasting Symphony. Cambridge University Press, Cambridge, 2020. [19] [第十一作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and K. Sato. Ronkin/Zeta Correspondence. arXiv, arXiv:2212.13704, 2022. |
| References_xml | – reference: [46] S. E. Venegas-Andraca. Quantum walks: A comprehensive review. Quantum Information Processing, Vol. 11, pp. 1015–1106, 2012. – reference: [45] 竹居正登． 入門 確率過程． 森北出版，東京， 2020. – reference: [21] [第八作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and S. Tamura. Mahler/Zeta Correspondence. Quantum Information Processing, Vol. 21, 298, 2022. – reference: [38] K. Manouchehri, and J. Wang. Physical Implementation of Quantum Walks. Springer, New York, 2014. – reference: [12] [第零作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice. Yokohama Mathematical Journal, Vol. 67, pp. 115–123, 2021. – reference: [11] [第十作品：ゼータ対応] C. Kiumi, N. Konno, and Y. Oshima. IPS/Zeta correspondence for the Domany–Kinzel model. Interdisciplinary Information Sciences (in press), arXiv, arXiv:2206.03188, 2022. – reference: [1] J. Akahori, N. Konno, and I. Sato. Absolute Zeta functions for Zeta functions of quantum cellular automata. Quantum Information and Computation, Vol. 23, pp. 1261–1274, 2023. – reference: [4] S. Attal, F. Petruccione, and I. Sinayskiy. Open quantum walks on graphs. Physics Letters A, Vol. 376, pp. 1545–1548, 2012. – reference: [9] R. Durrett. Lecture Notes on Particle Systems and Percolation. Wadsworth, Inc., California, 1988. – reference: [25] 今野紀雄． 量子ウォーク． 森北出版，東京， 2014. – reference: [43] R. B．シナジ． マルコフ連鎖から格子確率モデルへ． 丸善出版，東京， 2012. – reference: [41] R. Portugal. Quantum Walks and Search Algorithms (2nd edition). Springer, New York, 2018. – reference: [44] F. Spitzer. Principles of Random Walk (2nd edition). Springer, New York, 1976. – reference: [2] 青山崇洋． 多重ゼータ関数と高次元ランダムウォーク． 応用数理, Vol. 33, No. 2, pp. 62–71, 2023. – reference: [34] 黒川信重． 絶対ゼータ関数論． 岩波書店，東京， 2016. – reference: [5] F. Brunault, and W. Zudilin. Many Variations of Mahler Measures: A Lasting Symphony. Cambridge University Press, Cambridge, 2020. – reference: [27] 今野紀雄． 量子探索―量子ウォークが拓く最先端アルゴリズム―． 近代科学社，東京， 2021. – reference: [39] J. McKee, and C. Smyth. Around the Unit Circle: Mahler Measure, Integer Matrices and Roots of Unity. Springer, Cham, 2021. – reference: [22] 今野紀雄． 量子ウォークの数理． 産業図書，東京， 2008. – reference: [35] 黒川信重． 絶対数学原論． 現代数学社，京都， 2016. – reference: [6] G. Chinta, J. Jorgenson, and A. Karlsson. Heat kernels on regular graphs and generalized Ihara zeta function formulas. Monatshefte fur Mathematik, Vol. 178, pp. 171–190, 2015. – reference: [8] E. Domany, and W. Kinzel. Equivalence of cellular automata to Ising models and directed percolation. Physical Review Letters, Vol. 53, pp. 311–314, 1984. – reference: [14] [第三作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. IPS/Zeta Correspondence. Quantum Information and Computation, Vol. 22, pp. 251–269, 2022. – reference: [37] 町田拓也． 量子ウォーク―基礎と数理―. 裳華房，東京， 2018. – reference: [10] [第九作品：ゼータ対応] Y. Ide, T. Komatsu, N. Konno, and I. Sato. Metzler/Zeta Correspondence. Discrete Mathematics, Vol. 346, 113418, 2023. – reference: [26] 今野紀雄． 量子ウォークによる時系列解析． 日本評論社，東京， 2020. – reference: [36] 町田拓也． 図で解る量子ウォーク入門． 森北出版，東京， 2015. – reference: [18] [第十二作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Alternating Walk/Zeta Correspondence. arXiv, arXiv:2302.09583, 2023. – reference: [24] N. Konno. Quantum walks. In Quantum Potential Theory (edited by U. Franz and M. Schurmann), Lecture Notes in Mathematics, Vol. 1954, pp. 309–452, Springer-Verlag, Heidelberg, 2008. – reference: [30] N. Konno. On the relation between quantum walks and absolute zeta functions. Quantum Studies: Mathematics and Foundations, Vol. 11, pp. 147–157, 2024. – reference: [7] B. Clair. The Ihara zeta function of the infinite grid. Electronic Journal of Combinatorics, Vol. 21, Paper 2.16, 2014. – reference: [32] N. Konno, and I. Sato. On the relation between quantum walks and zeta functions. Quantum Information Processing, Vol. 11, pp. 341–349, 2012. – reference: [13] [第一作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Grover/Zeta Correspondence based on the Konno-Sato theorem. Quantum Information Processing, Vol. 20, 268, 2021. – reference: [40] J. R. Norris. Markov Chains. Cambridge University Press, Cambridge, 1997. – reference: [42] P. Ren, T. Aleksic, D. Emms, R. C. Wilson, and E. R. Hancock. Quantum walks, Ihara zeta functions and cospectrality in regular graphs. Quantum Information Processing, Vol. 10, pp. 405–417, 2011. – reference: [20] [第七作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and S. Tamura. A generalized Grover/Zeta Correspondence. arXiv, arXiv:2201.03973, 2022. – reference: [28] N. Konno. An analogue of the Riemann Hypothesis via quantum walks. Quantum Studies: Mathematics and Foundations, Vol. 9, pp. 367–379, 2022. – reference: [31] 今野紀雄・井手勇介（共編著）． 量子ウォークの新展開． 培風館，東京， 2019. – reference: [3] S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy. Open quantum random walks. Journal of Statistical Physics, Vol. 147, pp. 832–852, 2012. – reference: [33] [第六作品：ゼータ対応] N. Konno, and S. Tamura. Walk/Zeta Correspondence for quantum and correlated random walks. Yokohama Mathematical Journal, Vol. 67, pp. 125–152, 2021. – reference: [15] [第四作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Vertex-Face/Zeta Correspondence. Journal of Algebraic Combinatorics, Vol. 56, pp. 527–545, 2022. – reference: [23] 今野紀雄． 無限粒子系の科学． 講談社，東京， 2008. – reference: [19] [第十一作品：ゼータ対応] T. Komatsu, N. Konno, I. Sato, and K. Sato. Ronkin/Zeta Correspondence. arXiv, arXiv:2212.13704, 2022. – reference: [29] 今野紀雄． 量子ウォークからゼータ対応へ―ゼータ関数を通して眺める数理モデル―． 日本評論社，東京， 2022. – reference: [16] [第五作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. CTM/Zeta Correspondence. Quantum Studies: Mathematics and Foundations, Vol. 9, pp. 165–173, 2022. – reference: [17] [第二作品：ゼータ対応] T. Komatsu, N. Konno, and I. Sato. Walk/Zeta Correspondence. Journal of Statistical Physics, Vol. 190, 36, 2023. |
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| Title | ゼータ対応の数理 |
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