D.M.S. Bagguley, Editor, Pulsed Magnetic Resonance: NMR, ESR, and Optics. A recognition of E.L. Hahn. Oxford
University Press, Oxford, New York, Toronto 1992
O. Baumgart, The Quadratic Reciprocity Law: A Collection of Classical Proofs. Birkhäuser and Springer, Cham,
Heidelberg, New York, Dordrecht, London 2015
K. Burde, Ein rationales biquadratisches Reziprozitätsgesetz. J. Reine und Angew. Math. 235, 175-184 (1969)
J.C. Carr, T.J. Carroll, Magnetic Resonance Angiography, Principles and Applications. Springer New York, Dordrecht, Heidelberg, London 2012
C. Chevalley, The Algebraic Theory of Spinors and Clifford Algebras. Collected Works, Volume 2, SpringerVerlag, Berlin, Heidelberg, New York 1997
N. Childress, Class Field Theory. Springer-Verlag, Berlin, Heidelberg, New York 2009
C.W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. American Mathematical
Society, Providence, Rhode Island 1999
J.A. Dieudonné, Review of The Algebraic Theory of Spinors by C. Chevalley. Bull. Amer. Math. Soc. 60, 408-413
(1954)
J. Franchi, Y. Le Jan, Hyperbolic Dynamics and Brownian Motion: An Introduction. Oxford University Press,
Oxford, New York 2012
L.J. Goldstein, Analytic Number Theory. Prentice Hall, Englewood Cliffs, New Jersey 1971
G. Gras, Class Field Theory: From Theory to Practice. Springer-Verlag, Berlin, Heidelberg, NewYork 2005
V.W. Guillemin, Symplectic spinors and partial differential equations. In: Géomeétrie Symplectique et Physique
Mathématique, pp. 217-252, Centre National de la Recherche Scientifique, Paris 1975
V.W. Guillemin, S. Sternberg, Supersymmetry and Equivariant de Rham Theory. Springer-Verlag, Berlin, Heidelberg, New York 1999
D. Harari, Galois Cohomology and Class Field Theory. Springer Nature, Cham, Switzerland 2020
R. Howe, On the role of the Heisenberg group in harmonic analysis. Bull. Amer. Math. Soc. (New Series), Vol. 3,
821-843 (1980)
R. Howe, Quantum mechanics and partial differential equations. J. Funct. Anal. 38, 188-254 (1980)
R. Howe, The oscillator semigroup. In: The Mathematical Heritage of Hermann Weyl. R.O. Wells, Jr., Editor,
Proceedings of Symposia in Pure Mathematics, Vol. 48, pp. 61-132, American Mathematical Society, Providence,
Rhode Island 1988
H. Johansen-Berg, T.E.J. Behrens, Editors, Diffusion MRI: From Quantitative Measurement to In vivo Neuroanatomy. Elsevier, Academic Press, Amsterdam, Boston, Heidelberg 2009
D.K. Jones, Editor, Diffusion MRI: Theory, Methods, and Applications. Oxford University Press, Oxford, New
York 2010
B. Kostant, Symplectic spinors. In: Istituto Nazionale di Alta Matematica Roma, Symposia Mathematica, Volume
XIV, pp. 139–152, Academic Press, London, New York 1974
S. Lang, Introduction to Algebraic and Abelian Functions. Second edition, Springer-Verlag, New York, Heidelberg, Berlin 1987
G. Lion, M. Vergne, The Weil Representation, Maslov Index and Theta Series. Birkhäuser Verlag, Boston, Basel,
Stuttgart 1980
A. Merkurjev, On the norm residue symbol of degree 2. Sovjet Math. Doklady 24, 546-551 (1981)
P. Morandi, Field and Galois Theory. Springer-Verlag, New York, Berlin, Heidelberg 1996
S. Mori, Introduction to Diffusion Tensor Imaging. Elsevier, Amsterdam, Boston, Heidelberg 2007
J. Neukirch, Class Field Theory. Springer-Verlag, Berlin, Heidelberg, New York 1986
A.M. Ozorio de Almeida, Entanglement in phase space. In: Entanglement and Decoherence: Foundations and
Modern Trends, A. Buchleitner, C. Viviescas, M. Tiersch, Editors, Lecture Notes in Physics 768, pp. 157-219,
Springer-Verlag, Berlin, Heidelberg, New York 2010
R.S. Pierce, Associative Algebras. Springer-Verlag, New York, Heidelberg, Berlin 1982
C.R. Riehm, Introduction to Orthogonal, Symplectic and Unitary Representations of Finite Groups. American
Mathematical Society, Providence, Rhode Island 2011
H. Salzmann, D. Betten, T. Grundhöfer, H. Hähl, R. Löwen, M. Stroppel, Compact Projective Planes, With an
Introduction to Octonion Geometry. Walter de Gruyter, Berlin, New York 1995
W. Scharlau, Quadratic and Hermitian Forms. Springer-Verlag, Berlin, Heidelberg, New York 1985
W.J. Schempp, Magnetic Resonance Imaging: Mathematical Foundations and Applications. Wiley-Liss, New
York, Chichester, Weinheim 1998
W.J. Schempp, Dynamic metaplectic spinor quantization: The projective correspondence for spectral dual pairs. Journal of Applied Mathematics and Computing 59, 545-584 (2019)
W.J. Schempp, Applications of metaplectic cohomology and global-local contact holonomy. Journal of Applied Mathematics and Computing 67 (2), 2021
E.O. Stejskal, Use of spin echoes in a pulsed magnetic-field gradient to study non-isotropic, restricted diffusion
and flow. J. Chem. Phys. 43, 3597-3603 (1965)
E.O. Stejskal, J.E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field
gradient. J. Chem. Phys. 42, 288-292 (1965)
A. Weil, Basic Number Theory. Third edition, Springer-Verlag, Berlin, Heidelberg, New York 1974
A. Weil, Sur certains groupes d’opérateurs unitaires. Acta Math. 111, 143–211 (1964); Collected Papers, Vol. III,
pp. 1-69, Springer-Verlag, New York, Heidelberg, Berlin 1979
A. Weil, Sur la formule de Siegel dans la théorie des groupes classiques. Acta Math. 113, 1-87 (1965); Collected
Papers, Vol. III, pp. 71-157, Springer-Verlag, New York, Heidelberg, Berlin 1979
Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement
The purpose of the paper is to elucidate the cyclotomographic applications of the coadjoint orbit methodology to the Legendre-Hilbert-Artin symbolic tower of class field theory in the sense of the theories of Chevalley, Hasse, Weil and Witt. The Witt arithmetics concludes with the law of rational biquadratic reciprocity and quantum entanglement.
The purpose of the paper is to elucidate the cyclotomographic applications of the coadjoint orbit methodology to the Legendre-Hilbert-Artin symbolic tower of class field theory in the sense of the theories of Chevalley, Hasse, Weil and Witt. The Witt arithmetics concludes with the law of rational biquadratic reciprocity and quantum entanglement.
D.M.S. Bagguley, Editor, Pulsed Magnetic Resonance: NMR, ESR, and Optics. A recognition of E.L. Hahn. Oxford
University Press, Oxford, New York, Toronto 1992
O. Baumgart, The Quadratic Reciprocity Law: A Collection of Classical Proofs. Birkhäuser and Springer, Cham,
Heidelberg, New York, Dordrecht, London 2015
K. Burde, Ein rationales biquadratisches Reziprozitätsgesetz. J. Reine und Angew. Math. 235, 175-184 (1969)
J.C. Carr, T.J. Carroll, Magnetic Resonance Angiography, Principles and Applications. Springer New York, Dordrecht, Heidelberg, London 2012
C. Chevalley, The Algebraic Theory of Spinors and Clifford Algebras. Collected Works, Volume 2, SpringerVerlag, Berlin, Heidelberg, New York 1997
N. Childress, Class Field Theory. Springer-Verlag, Berlin, Heidelberg, New York 2009
C.W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. American Mathematical
Society, Providence, Rhode Island 1999
J.A. Dieudonné, Review of The Algebraic Theory of Spinors by C. Chevalley. Bull. Amer. Math. Soc. 60, 408-413
(1954)
J. Franchi, Y. Le Jan, Hyperbolic Dynamics and Brownian Motion: An Introduction. Oxford University Press,
Oxford, New York 2012
L.J. Goldstein, Analytic Number Theory. Prentice Hall, Englewood Cliffs, New Jersey 1971
G. Gras, Class Field Theory: From Theory to Practice. Springer-Verlag, Berlin, Heidelberg, NewYork 2005
V.W. Guillemin, Symplectic spinors and partial differential equations. In: Géomeétrie Symplectique et Physique
Mathématique, pp. 217-252, Centre National de la Recherche Scientifique, Paris 1975
V.W. Guillemin, S. Sternberg, Supersymmetry and Equivariant de Rham Theory. Springer-Verlag, Berlin, Heidelberg, New York 1999
D. Harari, Galois Cohomology and Class Field Theory. Springer Nature, Cham, Switzerland 2020
R. Howe, On the role of the Heisenberg group in harmonic analysis. Bull. Amer. Math. Soc. (New Series), Vol. 3,
821-843 (1980)
R. Howe, Quantum mechanics and partial differential equations. J. Funct. Anal. 38, 188-254 (1980)
R. Howe, The oscillator semigroup. In: The Mathematical Heritage of Hermann Weyl. R.O. Wells, Jr., Editor,
Proceedings of Symposia in Pure Mathematics, Vol. 48, pp. 61-132, American Mathematical Society, Providence,
Rhode Island 1988
H. Johansen-Berg, T.E.J. Behrens, Editors, Diffusion MRI: From Quantitative Measurement to In vivo Neuroanatomy. Elsevier, Academic Press, Amsterdam, Boston, Heidelberg 2009
D.K. Jones, Editor, Diffusion MRI: Theory, Methods, and Applications. Oxford University Press, Oxford, New
York 2010
B. Kostant, Symplectic spinors. In: Istituto Nazionale di Alta Matematica Roma, Symposia Mathematica, Volume
XIV, pp. 139–152, Academic Press, London, New York 1974
S. Lang, Introduction to Algebraic and Abelian Functions. Second edition, Springer-Verlag, New York, Heidelberg, Berlin 1987
G. Lion, M. Vergne, The Weil Representation, Maslov Index and Theta Series. Birkhäuser Verlag, Boston, Basel,
Stuttgart 1980
A. Merkurjev, On the norm residue symbol of degree 2. Sovjet Math. Doklady 24, 546-551 (1981)
P. Morandi, Field and Galois Theory. Springer-Verlag, New York, Berlin, Heidelberg 1996
S. Mori, Introduction to Diffusion Tensor Imaging. Elsevier, Amsterdam, Boston, Heidelberg 2007
J. Neukirch, Class Field Theory. Springer-Verlag, Berlin, Heidelberg, New York 1986
A.M. Ozorio de Almeida, Entanglement in phase space. In: Entanglement and Decoherence: Foundations and
Modern Trends, A. Buchleitner, C. Viviescas, M. Tiersch, Editors, Lecture Notes in Physics 768, pp. 157-219,
Springer-Verlag, Berlin, Heidelberg, New York 2010
R.S. Pierce, Associative Algebras. Springer-Verlag, New York, Heidelberg, Berlin 1982
C.R. Riehm, Introduction to Orthogonal, Symplectic and Unitary Representations of Finite Groups. American
Mathematical Society, Providence, Rhode Island 2011
H. Salzmann, D. Betten, T. Grundhöfer, H. Hähl, R. Löwen, M. Stroppel, Compact Projective Planes, With an
Introduction to Octonion Geometry. Walter de Gruyter, Berlin, New York 1995
W. Scharlau, Quadratic and Hermitian Forms. Springer-Verlag, Berlin, Heidelberg, New York 1985
W.J. Schempp, Magnetic Resonance Imaging: Mathematical Foundations and Applications. Wiley-Liss, New
York, Chichester, Weinheim 1998
W.J. Schempp, Dynamic metaplectic spinor quantization: The projective correspondence for spectral dual pairs. Journal of Applied Mathematics and Computing 59, 545-584 (2019)
W.J. Schempp, Applications of metaplectic cohomology and global-local contact holonomy. Journal of Applied Mathematics and Computing 67 (2), 2021
E.O. Stejskal, Use of spin echoes in a pulsed magnetic-field gradient to study non-isotropic, restricted diffusion
and flow. J. Chem. Phys. 43, 3597-3603 (1965)
E.O. Stejskal, J.E. Tanner, Spin diffusion measurements: Spin echoes in the presence of a time-dependent field
gradient. J. Chem. Phys. 42, 288-292 (1965)
A. Weil, Basic Number Theory. Third edition, Springer-Verlag, Berlin, Heidelberg, New York 1974
A. Weil, Sur certains groupes d’opérateurs unitaires. Acta Math. 111, 143–211 (1964); Collected Papers, Vol. III,
pp. 1-69, Springer-Verlag, New York, Heidelberg, Berlin 1979
A. Weil, Sur la formule de Siegel dans la théorie des groupes classiques. Acta Math. 113, 1-87 (1965); Collected
Papers, Vol. III, pp. 71-157, Springer-Verlag, New York, Heidelberg, Berlin 1979
Schempp, W. J. (2021). Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement. Constructive Mathematical Analysis, 4(1), 61-80. https://doi.org/10.33205/cma.804852
AMA
Schempp WJ. Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement. CMA. March 2021;4(1):61-80. doi:10.33205/cma.804852
Chicago
Schempp, Walter J. “Congruence and Metaplectic Covariance: Rational Biquadratic Reciprocity and Quantum Entanglement”. Constructive Mathematical Analysis 4, no. 1 (March 2021): 61-80. https://doi.org/10.33205/cma.804852.
W. J. Schempp, “Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement”, CMA, vol. 4, no. 1, pp. 61–80, 2021, doi: 10.33205/cma.804852.
ISNAD
Schempp, Walter J. “Congruence and Metaplectic Covariance: Rational Biquadratic Reciprocity and Quantum Entanglement”. Constructive Mathematical Analysis 4/1 (March 2021), 61-80. https://doi.org/10.33205/cma.804852.
JAMA
Schempp WJ. Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement. CMA. 2021;4:61–80.
MLA
Schempp, Walter J. “Congruence and Metaplectic Covariance: Rational Biquadratic Reciprocity and Quantum Entanglement”. Constructive Mathematical Analysis, vol. 4, no. 1, 2021, pp. 61-80, doi:10.33205/cma.804852.
Vancouver
Schempp WJ. Congruence and metaplectic covariance: Rational biquadratic reciprocity and quantum entanglement. CMA. 2021;4(1):61-80.