메뉴 건너뛰기




Volumn 10, Issue , 2008, Pages

A quantum mechanical model of the Riemann zeros

Author keywords

[No Author keywords available]

Indexed keywords

HAMILTONIANS; PHASE SPACE METHODS; WINDOWS OPERATING SYSTEM;

EID: 46249103793     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/10/3/033016     Document Type: Article
Times cited : (29)

References (40)
  • 5
    • 0042584143 scopus 로고    scopus 로고
    • The Riemann Hypothesis
    • Conrey J B 2003 The Riemann Hypothesis Not. Am. Math. Soc. 50 341-53
    • (2003) Not. Am. Math. Soc , vol.50 , pp. 341-353
    • Conrey, J.B.1
  • 6
    • 0038016775 scopus 로고    scopus 로고
    • Rosu H C 2003 Quantum Hamiltonians and prime numbers Mod. Phys. Lett. A 18 1205 (Preprint quant-ph/0304139)
    • Rosu H C 2003 Quantum Hamiltonians and prime numbers Mod. Phys. Lett. A 18 1205 (Preprint quant-ph/0304139)
  • 7
    • 0038475895 scopus 로고    scopus 로고
    • Elizalde E, Moretti V and Zerbini S 2003 On recent strategies proposed for proving the Riemann hypothesis Int. J. Mod. Phys. A 18 2189-96 (Preprint math-ph/0109006)
    • Elizalde E, Moretti V and Zerbini S 2003 On recent strategies proposed for proving the Riemann hypothesis Int. J. Mod. Phys. A 18 2189-96 (Preprint math-ph/0109006)
  • 8
    • 0002350116 scopus 로고
    • Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
    • Selberg A 1956 Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series J. Indian Math. Soc. 20 47-87
    • (1956) J. Indian Math. Soc , vol.20 , pp. 47-87
    • Selberg, A.1
  • 9
    • 0000308274 scopus 로고
    • The pair correlation of zeros of the zeta function
    • Providence, RI: American Mathematical Society
    • Montgomery H L 1973 The pair correlation of zeros of the zeta function Analytic Number Theory (Providence, RI: American Mathematical Society)
    • (1973) Analytic Number Theory
    • Montgomery, H.L.1
  • 10
    • 0004163930 scopus 로고    scopus 로고
    • Amsterdam: Elsevier Academic
    • Mehta M L 2004 Random Matrices (Amsterdam: Elsevier Academic)
    • (2004) Random Matrices
    • Mehta, M.L.1
  • 11
    • 84968518845 scopus 로고
    • On the distribution of spacings between zeros of zeta functions
    • Odlyzko A 1987 On the distribution of spacings between zeros of zeta functions Math. Comput. 48 273
    • (1987) Math. Comput , vol.48 , pp. 273
    • Odlyzko, A.1
  • 12
    • 0010963569 scopus 로고
    • Quantum Chaos and Statistical Nuclear Physics
    • ed T H Seligman and H Nishioka New York: Springer
    • Berry M V 1986 Quantum Chaos and Statistical Nuclear Physics (Lecture Notes in Physics no. 263) ed T H Seligman and H Nishioka (New York: Springer)
    • (1986) Lecture Notes in Physics , vol.263
    • Berry, M.V.1
  • 14
    • 0001397592 scopus 로고
    • Periodic orbits and classical quantization conditions
    • Gutzwiller M C 1971 Periodic orbits and classical quantization conditions J. Math. Phys. 12 343-58
    • (1971) J. Math. Phys , vol.12 , pp. 343-358
    • Gutzwiller, M.C.1
  • 15
    • 53149152987 scopus 로고    scopus 로고
    • Connes A 1999 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function Selecta Math. 5 29 (Preprint math.NT/9811068)
    • Connes A 1999 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function Selecta Math. 5 29 (Preprint math.NT/9811068)
  • 17
    • 0032647538 scopus 로고    scopus 로고
    • The Riemann zeros and eigenvalue asymptotics
    • Berry M V and Keating J P 1999 The Riemann zeros and eigenvalue asymptotics SIAM Rev. 41 236
    • (1999) SIAM Rev , vol.41 , pp. 236
    • Berry, M.V.1    Keating, J.P.2
  • 18
    • 33645690479 scopus 로고    scopus 로고
    • Sierra G 2005 The Riemann zeros and the cyclic renormalization group J. Stat. Mech. P12006 (Preprint math.NT/0510572)
    • Sierra G 2005 The Riemann zeros and the cyclic renormalization group J. Stat. Mech. P12006 (Preprint math.NT/0510572)
  • 19
    • 34250736969 scopus 로고    scopus 로고
    • Sierra G 2007 H = xp with interaction and the Riemann zeros Nucl. Phys. B 776 327 (Preprint math-ph/0702034)
    • Sierra G 2007 H = xp with interaction and the Riemann zeros Nucl. Phys. B 776 327 (Preprint math-ph/0702034)
  • 20
    • 46249089266 scopus 로고    scopus 로고
    • Sierra G 2007 Quantum reconstruction of the Riemann zeta function J. Phys. A: Math. Theor. 40 1 (Preprint 0711.1. 1063)
    • Sierra G 2007 Quantum reconstruction of the Riemann zeta function J. Phys. A: Math. Theor. 40 1 (Preprint 0711.1. 1063)
  • 21
    • 1442312675 scopus 로고    scopus 로고
    • Russian doll renormalization group and superconductivity
    • Preprint cond-mat/0211338
    • LeClair A, RomáJ M and Sierra G 2004 Russian doll renormalization group and superconductivity Phys. Rev. B 69 (Preprint cond-mat/0211338)
    • (2004) Phys. Rev. B , vol.69
    • LeClair, A.1    RomáJ, M.2    Sierra, G.3
  • 22
    • 21244500127 scopus 로고    scopus 로고
    • The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity
    • Preprint cond-mat/0503014
    • Anfossi A, LeClair A and Sierra G 2005 The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity J. Stat. Mech. P05011 (Preprint cond-mat/0503014)
    • (2005) J. Stat. Mech
    • Anfossi, A.1    LeClair, A.2    Sierra, G.3
  • 23
    • 8744255371 scopus 로고    scopus 로고
    • Dunning C and Links J 2004 Integrability of the Russian doll BCS model Nucl. Phys. B 702 481 (Preprint cond-mat/0406234)
    • Dunning C and Links J 2004 Integrability of the Russian doll BCS model Nucl. Phys. B 702 481 (Preprint cond-mat/0406234)
  • 24
    • 34250760564 scopus 로고    scopus 로고
    • Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis
    • Preprint math-ph/0611043
    • LeClair A 2006 Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis Preprint math-ph/0611043
    • (2006)
    • LeClair, A.1
  • 25
    • 33845912950 scopus 로고    scopus 로고
    • Twamley J and Milburn G J 2006 The quantum Mellin transform New J. Phys. 8 328 (Preprint quant-ph/0702107)
    • Twamley J and Milburn G J 2006 The quantum Mellin transform New J. Phys. 8 328 (Preprint quant-ph/0702107)
  • 26
    • 0035649980 scopus 로고    scopus 로고
    • Multiple zeta values at non-positive integers
    • Akiyama S and Tanigawa Y 2001 Multiple zeta values at non-positive integers Ramanujan J 5 327-51
    • (2001) Ramanujan J , vol.5 , pp. 327-351
    • Akiyama, S.1    Tanigawa, Y.2
  • 27
    • 34250742155 scopus 로고    scopus 로고
    • Renormalization of multiple zeta values
    • Preprint math.NT/0606076
    • Guo L and Zhang B 2006 Renormalization of multiple zeta values Preprint math.NT/0606076
    • (2006)
    • Guo, L.1    Zhang, B.2
  • 28
    • 0035585510 scopus 로고    scopus 로고
    • Bonneau G, Faraut J and Valent G 2001 Self-adjoint extensions of operators and the teaching of quantum mechanics Am. J. Phys. 69 322 (Preprint quant-ph/0103153)
    • Bonneau G, Faraut J and Valent G 2001 Self-adjoint extensions of operators and the teaching of quantum mechanics Am. J. Phys. 69 322 (Preprint quant-ph/0103153)
  • 29
    • 0000139548 scopus 로고
    • A new asymptotic representation for ζ(1/2+it) and quantum spectral determinants
    • Berry M V and Keating J P 1992 A new asymptotic representation for ζ(1/2+it) and quantum spectral determinants Proc. R. Soc. Lond. A 437 151
    • (1992) Proc. R. Soc. Lond. A , vol.437 , pp. 151
    • Berry, M.V.1    Keating, J.P.2
  • 30
    • 46249116239 scopus 로고    scopus 로고
    • Bombieri E A lower bound for the zeros of Riemanns zeta function on the critical line SéN. Bourbaki 1974-75 exp. no. 465 p 176-82
    • Bombieri E A lower bound for the zeros of Riemanns zeta function on the critical line SéN. Bourbaki 1974-75 exp. no. 465 p 176-82
  • 31
    • 0037583140 scopus 로고
    • Scattering theory and automorphic functions
    • Pavlov B S and Faddeev L D 1975 Scattering theory and automorphic functions Sov. Math. 3 522
    • (1975) Sov. Math , vol.3 , pp. 522
    • Pavlov, B.S.1    Faddeev, L.D.2
  • 33
    • 0000291634 scopus 로고
    • Stochastic behaviour in quantum scattering
    • Gutzwiller M C 1983 Stochastic behaviour in quantum scattering Physica D 7 341
    • (1983) Physica D , vol.7 , pp. 341
    • Gutzwiller, M.C.1
  • 34
    • 0038597392 scopus 로고    scopus 로고
    • Jost function, prime numbers and Riemann zeta function
    • Preprint math-ph/0303014
    • Joffily S 2003 Jost function, prime numbers and Riemann zeta function Preprint math-ph/0303014
    • (2003)
    • Joffily, S.1
  • 35
    • 4243778157 scopus 로고    scopus 로고
    • Bhaduri, R K, Avinash Khare and Law J 1995 Phase of the Riemann zeta function and the inverted harmonic oscillator Phys. Rev. E 52 486-91 (Preprint chao-dyn/9406006)
    • Bhaduri, R K, Avinash Khare and Law J 1995 Phase of the Riemann zeta function and the inverted harmonic oscillator Phys. Rev. E 52 486-91 (Preprint chao-dyn/9406006)
  • 36
    • 0038053088 scopus 로고    scopus 로고
    • Sur les espaces de Sonine associépar de Branges àla transformation de Fourier
    • Burnol J-F 2002 Sur les espaces de Sonine associépar de Branges àla transformation de Fourier C. R. Acad. Sci. Paris 335 689-92
    • (2002) C. R. Acad. Sci. Paris , vol.335 , pp. 689-692
    • Burnol, J.-F.1
  • 37
    • 30244541785 scopus 로고    scopus 로고
    • Des éde Dirac et de Schröpour la transformation de Fourier
    • Burnol J-F 2003 Des éde Dirac et de Schröpour la transformation de Fourier C. R. Acad. Sci. Paris 336 919-24
    • (2003) C. R. Acad. Sci. Paris , vol.336 , pp. 919-924
    • Burnol, J.-F.1
  • 38
    • 85039677545 scopus 로고    scopus 로고
    • Scattering, determinants, hyperfunctions in relation to F(1 -s)/ F(s)
    • Preprint math.NT/0602425
    • Burnol J-F 2006 Scattering, determinants, hyperfunctions in relation to F(1 -s)/ F(s) Preprint math.NT/0602425
    • (2006)
    • Burnol, J.-F.1
  • 39
    • 46249096371 scopus 로고    scopus 로고
    • Burnol J F 2008 On some bound and scattering states associated with cosine kernel Preprint 0801.0530
    • Burnol J F 2008 On some bound and scattering states associated with cosine kernel Preprint 0801.0530
  • 40
    • 46249097982 scopus 로고    scopus 로고
    • Sierra G and Townsend P K in preparation
    • Sierra G and Townsend P K in preparation


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.