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Volumn 132, Issue 1, 1998, Pages 1-72

Ergodic theory on SL(n), diophantine approximations and anomalies in the lattice point problem

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EID: 0032382643     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050217     Document Type: Article
Times cited : (44)

References (60)
  • 1
    • 0040206856 scopus 로고
    • Statistical sums in optimization and computational problems
    • [B] Barvinok, A.U.: Statistical sums in optimization and computational problems, Algebra Analiz 4, No. 1, (1992) 3-53; English transl.: St. Petersburg Math. J., 4, No. 1, 1-42 (1993)
    • (1992) Algebra Analiz , vol.4 , Issue.1 , pp. 3-53
    • Barvinok, A.U.1
  • 2
    • 0040206863 scopus 로고
    • English transl
    • [B] Barvinok, A.U.: Statistical sums in optimization and computational problems, Algebra Analiz 4, No. 1, (1992) 3-53; English transl.: St. Petersburg Math. J., 4, No. 1, 1-42 (1993)
    • (1993) St. Petersburg Math. J. , vol.4 , Issue.1 , pp. 1-42
  • 3
    • 0038569422 scopus 로고
    • Randomness of n√2mod1 and a Ramsey property of the hyperbola
    • [Bel] Beck, J.: Randomness of n√2mod1 and a Ramsey property of the hyperbola, Colloquia Math. Soc. János Bolyai (Budapest), 60, 23-66 (1991)
    • (1991) Colloquia Math. Soc. János Bolyai (Budapest) , vol.60 , pp. 23-66
    • Beck, J.1
  • 4
    • 0010091163 scopus 로고
    • Probabilistic diophantine approximation. Part I. Kronecker sequences
    • Beck, J.: Probabilistic diophantine approximation. Part I. Kronecker sequences, Ann. of Math., 140, No. 2, 109-160 (1994)
    • (1994) Ann. of Math. , vol.140 , Issue.2 , pp. 109-160
    • Beck, J.1
  • 8
    • 0003315273 scopus 로고
    • Multi-dimensional continued fraction algorithms
    • Amsterdam
    • [Br] Brentjes A.J.: Multi-dimensional continued fraction algorithms, Math. Centree Tracts, 145, Amsterdam, 1981
    • (1981) Math. Centree Tracts , vol.145
    • Brentjes, A.J.1
  • 9
    • 0040206843 scopus 로고
    • On the bounds of quadratic discrepancies of certain lattice grids, in: Numerical methods in the problems of mathematical physics and cybernetics
    • in Russian
    • [By] Bykovskii, V.A.: On the bounds of quadratic discrepancies of certain lattice grids, In: Numerical methods in the problems of mathematical physics and cybernetics, DVO AN SSSR, Vladivostok, p. 3-14 (in Russian) 1987
    • (1987) DVO AN SSSR, Vladivostok , pp. 3-14
    • Bykovskii, V.A.1
  • 10
    • 0040206837 scopus 로고
    • A general ergodic theorem
    • [Cal] Calderon, A.P.: A general ergodic theorem, Ann. of Math., 58, No. 1, 182-191 (1953)
    • (1953) Ann. of Math. , vol.58 , Issue.1 , pp. 182-191
    • Calderon, A.P.1
  • 15
    • 0040801173 scopus 로고
    • English transl.: Springer-Verlag, Berlin etc.
    • [CFS] Cornfeld, I.P., Fomin, S.V., Sinai, Ya. G.: Ergodic Theory, Nauka, Moscow (1980); English transl.: Springer-Verlag, Berlin etc., 1982
    • (1982)
  • 16
    • 84961490968 scopus 로고
    • Divergent trajectories of flows on homogeneous spaces and diophantine approximation
    • Dani, S.G.: Divergent trajectories of flows on homogeneous spaces and diophantine approximation, J. reine und angew. Math., 359, 55-89 (1985)
    • (1985) J. Reine und Angew. Math. , vol.359 , pp. 55-89
    • Dani, S.G.1
  • 17
    • 0040801172 scopus 로고
    • The theory of irrationalities of the 3-rd degree
    • Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the 3-rd degree, Proc. Steklov Math. Inst. 11 (1940); English translation, Translation of Mathematical Monographs, 10, Amer. Math. Soc. 1964
    • (1940) Proc. Steklov Math. Inst. , vol.11
    • Delone, B.N.1    Faddeev, D.K.2
  • 18
    • 0039615122 scopus 로고    scopus 로고
    • English translation
    • Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the 3-rd degree, Proc. Steklov Math. Inst. 11 (1940); English translation, Translation of Mathematical Monographs, 10, Amer. Math. Soc. 1964
    • Translation of Mathematical Monographs , vol.10
  • 19
    • 0003744099 scopus 로고
    • Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the 3-rd degree, Proc. Steklov Math. Inst. 11 (1940); English translation, Translation of Mathematical Monographs, 10, Amer. Math. Soc. 1964
    • (1964) Amer. Math. Soc.
  • 20
    • 0010760615 scopus 로고
    • Mean values of algebraic linear forms
    • Everest, G.R.; Mean values of algebraic linear forms, Proc. London Math. Soc., 70, No. 3 529-555 (1995)
    • (1995) Proc. London Math. Soc. , vol.70 , Issue.3 , pp. 529-555
    • Everest, G.R.1
  • 22
    • 84960567270 scopus 로고
    • Some problems of diophante approximation: The lattice points of a right-anled triangle: Parts I and II
    • Hardy, G.H., Littlewood, J.E.: Some problems of diophante approximation: the lattice points of a right-anled triangle: Parts I and II, Proc. London Math. Soc. (2), (1922) 20, 15-36; Abh. Math. Sem. Hamburg, 1, 212-249 (1922)
    • (1922) Proc. London Math. Soc. (2) , vol.20 , pp. 15-36
    • Hardy, G.H.1    Littlewood, J.E.2
  • 23
    • 84960567270 scopus 로고
    • Hardy, G.H., Littlewood, J.E.: Some problems of diophante approximation: the lattice points of a right-anled triangle: Parts I and II, Proc. London Math. Soc. (2), (1922) 20, 15-36; Abh. Math. Sem. Hamburg, 1, 212-249 (1922)
    • (1922) Abh. Math. Sem. Hamburg , vol.1 , pp. 212-249
  • 24
    • 0011885280 scopus 로고
    • Integrale auf konvexen Körpen I Monatsh
    • Hlawka, E.: Integrale auf konvexen Körpen I Monatsh. Math., 54, 1-36 1950
    • (1950) Math. , vol.54 , pp. 1-36
    • Hlawka, E.1
  • 25
    • 84963025636 scopus 로고
    • Exponential sums and lattice points. II
    • Huxley, M.N.: Exponential sums and lattice points. II Proc. London Math. Soc., 66, No. 2273-301 (1993)
    • (1993) Proc. London Math. Soc. , vol.66 , Issue.2 , pp. 273-301
    • Huxley, M.N.1
  • 26
    • 0002903209 scopus 로고
    • On the divisor and circle problem
    • Iwaniec, H.: Mozzochi, C.J.: On the divisor and circle problem, J. Number Theory, 29, No. 1, 60-93 (1988)
    • (1988) J. Number Theory , vol.29 , Issue.1 , pp. 60-93
    • Iwaniec, H.1    Mozzochi, C.J.2
  • 27
    • 0001071591 scopus 로고
    • Ein satz über Kettenbrüche, mit arithetischen Anwendungen
    • Khintchine, A.: Ein Satz über Kettenbrüche, mit arithetischen Anwendungen, Math. Zeitschrift, 18, 289-306 (1923)
    • (1923) Math. Zeitschrift , vol.18 , pp. 289-306
    • Khintchine, A.1
  • 30
    • 0000628957 scopus 로고
    • Lattice points in large convex bodies. II
    • Kratzel, E., Nowak, G.: Lattice points in large convex bodies. II, Acta Arithm., 62, No. 3, 285-295 (1992)
    • (1992) Acta Arithm. , vol.62 , Issue.3 , pp. 285-295
    • Kratzel, E.1    Nowak, G.2
  • 31
    • 0004249068 scopus 로고
    • Walter de Gruyter, Berlin-etc.
    • Krengel, U.: Ergodic theorems, Walter de Gruyter, Berlin-etc., 1985
    • (1985) Ergodic Theorems
    • Krengel, U.1
  • 32
    • 0040359769 scopus 로고
    • Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications to number theory
    • Kyoto, Springer-Verlag, Berlin Heidelberg, New York
    • Margulis, G.A.: Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications to number theory, Proc. Intern. Congress Math., 1990, Kyoto, pp. 194-215, Springer-Verlag, Berlin Heidelberg, New York, 1991
    • (1991) Proc. Intern. Congress Math., 1990 , pp. 194-215
    • Margulis, G.A.1
  • 33
    • 0011006992 scopus 로고
    • Ergodicity of flows on homogeneous spaces
    • Moore, C.C.: Ergodicity of flows on homogeneous spaces. Amer. J. Math., 88, 154-178 (1966)
    • (1966) Amer. J. Math. , vol.88 , pp. 154-178
    • Moore, C.C.1
  • 35
    • 0040206804 scopus 로고
    • Nombre de points d'un réseau dans un produit cartésien de domaines convexes
    • Série I
    • Nikichine, N.A., Skriganov M.M.: Nombre de points d'un réseau dans un produit cartésien de domaines convexes, C. R. Acad. Sci. Paris, 321, Série I, 671-675 (1995)
    • (1995) C. R. Acad. Sci. Paris , vol.321 , pp. 671-675
    • Nikichine, N.A.1    Skriganov, M.M.2
  • 37
    • 0001610084 scopus 로고
    • A lattice point problem: Parts I and II
    • Randol, B.: A lattice point problem: Parts I and II, Trans. Amer. Math. Soc., 121, 257-268 (1966); 125, 101-113 (1966)
    • (1966) Trans. Amer. Math. Soc. , vol.121 , pp. 257-268
    • Randol, B.1
  • 38
    • 84968509716 scopus 로고
    • Randol, B.: A lattice point problem: Parts I and II, Trans. Amer. Math. Soc., 121, 257-268 (1966); 125, 101-113 (1966)
    • (1966) Trans. Amer. Math. Soc. , vol.125 , pp. 101-113
  • 39
    • 0040206838 scopus 로고
    • The behavior under projection of dilating sets in a covering space
    • Randol, B.: The behavior under projection of dilating sets in a covering space, Trans. Amer. Math. Soc., 285, 855-859 (1984)
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 855-859
    • Randol, B.1
  • 41
    • 0040545510 scopus 로고
    • Interaction between ergodic theory, lie groups, and number theory
    • Zürich, Birkhaüser Verlag, Basel etc.
    • Ratner, M.: Interaction between ergodic theory, Lie groups, and number theory, Proc. Intern. Congress Math., 1994, Zürich, pp. 157-182, Birkhaüser Verlag, Basel etc., 1995
    • (1995) Proc. Intern. Congress Math., 1994 , pp. 157-182
    • Ratner, M.1
  • 42
    • 0003304303 scopus 로고
    • Diophantine approximation
    • Springer-Verlag, Berlin etc.
    • Schmidt, W.M.: Diophantine approximation, Lecture Notes in Math., 785, Springer-Verlag, Berlin etc., 1980
    • (1980) Lecture Notes in Math. , vol.785
    • Schmidt, W.M.1
  • 43
    • 0001680397 scopus 로고
    • A mean value theorem in geometry of numbers
    • Siegel, C.L.: A mean value theorem in geometry of numbers, Ann. of Math., 46, No. 2, 340-347 (1945)
    • (1945) Ann. of Math. , vol.46 , Issue.2 , pp. 340-347
    • Siegel, C.L.1
  • 44
    • 0038965164 scopus 로고
    • Lattices in algebraic number fields and uniform distributions modulo 1
    • Skriganov, M.M.: Lattices in algebraic number fields and uniform distributions modulo 1, Algebra Analiz, 1, No. 207-2282, (1989); English transl., Leningrad Math. J., 1, No. 2, 535-558 (1990)
    • (1989) Algebra Analiz , vol.1 , pp. 207-2282
    • Skriganov, M.M.1
  • 45
    • 0040206844 scopus 로고
    • English transl.
    • Skriganov, M.M.: Lattices in algebraic number fields and uniform distributions modulo 1, Algebra Analiz, 1, No. 207-2282, (1989); English transl., Leningrad Math. J., 1, No. 2, 535-558 (1990)
    • (1990) Leningrad Math. J. , vol.1 , Issue.2 , pp. 535-558
  • 46
    • 0039558056 scopus 로고
    • On integer points in polygons
    • Skriganov, M.M.: On integer points in polygons, Ann. Inst. Fourier, 43, No. 2, 313-323 (1993)
    • (1993) Ann. Inst. Fourier , vol.43 , Issue.2 , pp. 313-323
    • Skriganov, M.M.1
  • 48
    • 0013514968 scopus 로고
    • Skriganov, M.M.: Constructions of uniform distributions in terms of geometry of numbers Prépublication Inst. Fourier (1992), No. 200; Algebra Analiz., 6, No. 3, 200-230 (1994); Reprinted in St. Petersburg Math. J., 6, No. 3 635-664 (1995)
    • (1994) Algebra Analiz. , vol.6 , Issue.3 , pp. 200-230
  • 49
    • 37949025697 scopus 로고
    • Reprinted in
    • Skriganov, M.M.: Constructions of uniform distributions in terms of geometry of numbers Prépublication Inst. Fourier (1992), No. 200; Algebra Analiz., 6, No. 3, 200-230 (1994); Reprinted in St. Petersburg Math. J., 6, No. 3 635-664 (1995)
    • (1995) St. Petersburg Math. J. , vol.6 , Issue.3 , pp. 635-664
  • 50
    • 33748641556 scopus 로고    scopus 로고
    • Ergodic theory on homogeneous spaces and the lattice point counting for polyhedra
    • Skriganov, M.M.: Ergodic theory on homogeneous spaces and the lattice point counting for polyhedra, Doklady RAN, 355, 5 (1997), 220-225
    • (1997) Doklady Ran , vol.355 , Issue.5 , pp. 220-225
    • Skriganov, M.M.1
  • 51
    • 0040149448 scopus 로고
    • Anomalies in spectral asymptotics
    • Skriganov, M.M.: Anomalies in spectral asymptotics, Doklady RAN, 340, No. 5, 597-599(1995); English transl.: Doklady Mathematics, 51, No. 1, 104-106 (1995)
    • (1995) Doklady Ran , vol.340 , Issue.5 , pp. 597-599
    • Skriganov, M.M.1
  • 52
    • 0040206852 scopus 로고
    • English transl.
    • Skriganov, M.M.: Anomalies in spectral asymptotics, Doklady RAN, 340, No. 5, 597-599(1995); English transl.: Doklady Mathematics, 51, No. 1, 104-106 (1995)
    • (1995) Doklady Mathematics , vol.51 , Issue.1 , pp. 104-106
  • 53
    • 0039615116 scopus 로고    scopus 로고
    • On the littlwood-Paley theory for multidimensional fourier series
    • Skriganov, M.M.: On the Littlwood-Paley theory for multidimensional Fourier series, Zap. Nauchn. Semin. POMI, 226, 155-169 (1996); English transl.: Journal of Math. Sciences (Plenum Publish. Corporaton), to appear
    • (1996) Zap. Nauchn. Semin. POMI , vol.226 , pp. 155-169
    • Skriganov, M.M.1
  • 54
    • 0039615120 scopus 로고    scopus 로고
    • English transl.: Plenum Publish. Corporaton, to appear
    • Skriganov, M.M.: On the Littlwood-Paley theory for multidimensional Fourier series, Zap. Nauchn. Semin. POMI, 226, 155-169 (1996); English transl.: Journal of Math. Sciences (Plenum Publish. Corporaton), to appear
    • Journal of Math. Sciences
  • 56
    • 0040206854 scopus 로고
    • English transl.; V. H. Winston and Sons, Washington, D. C.
    • Sprindžuk, V.G.: Metric theory of diophantine approximations, Nauka, Moscow, 1977; English transl.; V. H. Winston and Sons, Washington, D. C., 1979
    • (1979)
  • 58
    • 84966240953 scopus 로고
    • On the number of lattice points in a compact n-dimensional polyhedron
    • Tarnopolska-Weiss, M.: On the number of lattice points in a compact n-dimensional polyhedron, Proc. Amer. Math. Soc., 74, 124-127 (1979)
    • (1979) Proc. Amer. Math. Soc. , vol.74 , pp. 124-127
    • Tarnopolska-Weiss, M.1
  • 59
    • 84967702091 scopus 로고
    • The ergodic theorem
    • Wiener, N. The ergodic theorem, Duke Math. J., 5, No. 1 1-18 (1939)
    • (1939) Duke Math. J. , vol.5 , Issue.1 , pp. 1-18
    • Wiener, N.1


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