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Volumn 229, Issue 1-3, 2001, Pages 29-55

Randomness in lattice point problems

Author keywords

Continued fraction; Discrepancy; Lattice points

Indexed keywords


EID: 0347040497     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(00)00200-4     Document Type: Article
Times cited : (21)

References (28)
  • 2
    • 0037893205 scopus 로고    scopus 로고
    • Diophantine approximation and quadratic fields
    • Gyory, Petho, Sós (Eds.), Walter de Gruyter GmbH, Berlin
    • J. Beck, Diophantine approximation and quadratic fields, in: Gyory, Petho, Sós (Eds.), Number Theory, Walter de Gruyter GmbH, Berlin, 1998, pp. 55-93.
    • (1998) Number Theory , pp. 55-93
    • Beck, J.1
  • 3
    • 77952944605 scopus 로고    scopus 로고
    • From probabilistic diophantine approximation to quadratic fields, Random and Quasi-Random Point Sets
    • Springer, New York
    • J. Beck, From probabilistic diophantine approximation to quadratic fields, Random and Quasi-Random Point Sets, Lecture Notes in Statistics, Vol. 138, Springer, New York, 1998, pp. 1-48.
    • (1998) Lecture Notes in Statistics , vol.138 , pp. 1-48
    • Beck, J.1
  • 4
    • 0010091163 scopus 로고
    • Probabilistic diophantine approximation-Part I: Kronecker sequences
    • J. Beck, Probabilistic diophantine approximation-Part I: Kronecker sequences, Ann. Math. 140 (1994) 451-502.
    • (1994) Ann. Math. , vol.140 , pp. 451-502
    • Beck, J.1
  • 7
    • 0011663110 scopus 로고
    • Irregularities of Distribution
    • Cambridge University Press, Cambridge
    • J. Beck, W.W.L. Chen, Irregularities of Distribution, Cambridge Tracts in Mathematics, Vol. 89, Cambridge University Press, Cambridge, 1987.
    • (1987) Cambridge Tracts in Mathematics , vol.89
    • Beck, J.1    Chen, W.W.L.2
  • 11
    • 0001790435 scopus 로고
    • On Roth's method in the theory of irregularities of point distributions
    • Academic Press, London
    • G. Halász, On Roth's method in the theory of irregularities of point distributions, Recent Progress in Analytic Number Theory, Vol. 2, Academic Press, London, 1981, pp. 79-94.
    • (1981) Recent Progress in Analytic Number Theory , vol.2 , pp. 79-94
    • Halász, G.1
  • 12
    • 0002429367 scopus 로고
    • The lattice-points of a right-angled triangle. I
    • G. Hardy, J. Littlewood, The lattice-points of a right-angled triangle. I, Proc. London Math. Soc. 3 (1920) 15-36.
    • (1920) Proc. London Math. Soc. , vol.3 , pp. 15-36
    • Hardy, G.1    Littlewood, J.2
  • 13
    • 0001445005 scopus 로고
    • The lattice-points of a right-angled triangle. II
    • G. Hardy, J. Littlewood, The lattice-points of a right-angled triangle. II, Abh. Math. Sem. Hamburg 1 (1922) 212-249.
    • (1922) Abh. Math. Sem. Hamburg , vol.1 , pp. 212-249
    • Hardy, G.1    Littlewood, J.2
  • 14
    • 0039972270 scopus 로고
    • Probability methods in some problems of analysis and number theory
    • M. Kac, Probability methods in some problems of analysis and number theory, Bull. Amer. Math. Soc. 55 (1949) 641-665.
    • (1949) Bull. Amer. Math. Soc. , vol.55 , pp. 641-665
    • Kac, M.1
  • 15
    • 0346122151 scopus 로고
    • Probability methods in the theory of distributions modulo one
    • J.H.B. Kemperman, Probability methods in the theory of distributions modulo one, Compositio Math. 16 (1964) 106-137.
    • (1964) Compositio Math. , vol.16 , pp. 106-137
    • Kemperman, J.H.B.1
  • 16
    • 0003918560 scopus 로고
    • (English translation) P. Noordhoff, Groningen, The Netherlands
    • A. Khintchine, Continued Fractions (English translation) P. Noordhoff, Groningen, The Netherlands 1963.
    • (1963) Continued Fractions
    • Khintchine, A.1
  • 17
    • 0001071591 scopus 로고
    • Ein Satz über Kettenbrüche mit arithmetischen Anwendungen
    • A. Khintchine, Ein Satz über Kettenbrüche mit arithmetischen Anwendungen, Math. Z. (1923) 289-306.
    • (1923) Math. Z. , pp. 289-306
    • Khintchine, A.1
  • 20
    • 0002817093 scopus 로고
    • Bemerkungen zur Theorie der Diophantischen Approximationen. I
    • A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximationen. I, Abh. Hamburg Sem. 1 (1922) 77-98.
    • (1922) Abh. Hamburg Sem. , vol.1 , pp. 77-98
    • Ostrowski, A.1
  • 21
    • 0002851522 scopus 로고
    • On irregularities of distribution
    • K.F. Roth, On irregularities of distribution, Mathematika 1 (1954) 73-79.
    • (1954) Mathematika , vol.1 , pp. 73-79
    • Roth, K.F.1
  • 22
    • 0037607113 scopus 로고
    • A metrical theorem in diophantine approximation
    • W.M. Schmidt, A metrical theorem in diophantine approximation, Canad. J. Math. 12 (1960) 619-631.
    • (1960) Canad. J. Math. , vol.12 , pp. 619-631
    • Schmidt, W.M.1
  • 23
    • 84968475578 scopus 로고
    • Metrical theorems on fractional parts of sequences
    • W.M. Schmidt, Metrical theorems on fractional parts of sequences, Trans. Amer. Math. Soc. 110 (1964) 493-518.
    • (1964) Trans. Amer. Math. Soc. , vol.110 , pp. 493-518
    • Schmidt, W.M.1
  • 24
    • 0039993069 scopus 로고
    • On the discrepancy of the sequence {nα}
    • V. Sós, On the discrepancy of the sequence {nα}, Coll. Math. Soc. János Bolyai 13 (1974) 359-367.
    • (1974) Coll. Math. Soc. János Bolyai , vol.13 , pp. 359-367
    • Sós, V.1
  • 25
    • 0347383157 scopus 로고
    • A sequence has almost nowhere small discrepancy
    • G. Tijdeman, G. Wagner, A sequence has almost nowhere small discrepancy, Monatshefte Math. 90 (1980) 315-329.
    • (1980) Monatshefte Math. , vol.90 , pp. 315-329
    • Tijdeman, G.1    Wagner, G.2
  • 26
    • 0037960194 scopus 로고
    • Über die Gleichverteilung von Zahlen mod Eins
    • H. Weyl, Über die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916) 313-352.
    • (1916) Math. Ann. , vol.77 , pp. 313-352
    • Weyl, H.1
  • 27
    • 0007543253 scopus 로고
    • Nombres de classes et fractions continues
    • Astérisque
    • D. Zagier, Nombres de classes et fractions continues, J. Arithmétiques Bordeaux, Astérisque (24-25) (1975) 81-97.
    • (1975) J. Arithmétiques Bordeaux , vol.24-25 , pp. 81-97
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.