Andrej Dujella:

Diofantske aproksimacije - Seminarske teme



1. Konačne diofantske aproksimacije

    J. Tong, The constant for finite Diophantine approximation, Fibonacci Quart. 35 (1997), 29-31.

    L. C. Eggan, On Diophantine approximations, Trans. Amer. Math. Soc. 99 (1961), 102-117.

2. Aproksimacije razlomcima specijalnog tipa

    C. Elsner, On the approximation of irrational numbers with rationals restricted by congruence relations, Fibonacci Quart. 34 (1996), 18-29.

    S. Uchiyama, On rational approximations to irrational numbers, Tsukuba J. Math. 4 (1980), 1-7.

    S. Hartman, Sur one condition supplementaire dans les approximations diophantiques, Colloq. Math. 2 (1951), 48-51.

    L. Kuipers, B. Meulenbed, Some properties of continued fractions, Acta Math. 87 (1952), 1-12.

3. Neka svojstva konstanti aproksimacije

    J. Jager, C. Kraaikamp, On the approximation by continued fractions, Indag. Math. 51 (1989), 289-307.

    J. Tong, A theorem on approximation of irrational numbers by simple continued fractions, Proc. Edinburg Math. Soc. 31 (1988), 197-204.

4. Verižni razlomci i Segreov teorem o asimetričnoj aproksimaciji

    J. Tong, Segre's theorem on asymmetric Diophantine approximation, J. Number Theory 28 (1988), 116-118.

    W. J. LeVeque, On asymmetric approximations, Michigan Math. J. 2 (1953), 1-6.

    J. Tong, A theorem on approximation of irrational numbers by simple continued fractions, Proc. Edinburg Math. Soc. 31 (1988), 197-204.

5. Schmidtova (alpha,beta)-igra

    W. M. Schmidt, Diophantine Approximation, Springer-Verlag, Berlin, 1980, 1996, pp. 48-59. (Ruski prijevod: Diofantovi približenija, Mir, Moskva, 1983, pp. 44-51.)

    W. M. Schmidt, On badly approximable numbers and certain games, Trans. Amer. Math. Soc. 123 (1966), 178-199.

6. Metrička teorija diofantskih aproksimacija

    J. W. S. Cassels, An Introduction to Diophantine Approximations, CUP, Cambridge, 1965, pp. 120-132.

    W. M. Schmidt, Diophantine Approximation, Springer-Verlag, Berlin, 1980, 1996, pp. 60-79. (Ruski prijevod: Diofantovi približenija, Mir, Moskva, 1983, pp. 51-64.)

    A. Ja. Hincin, Cepnye drobi, Fizmatgiz, Moskva, 1961, pp. 66-89.

7. Primjena LLL-algoritma na diofantske aproksimacije

    R. Tijdeman, Diophantine equations and Diophantine approximations, University of Leiden, 1988, pp. 10-18.

    A. K. Lenstra, H. W. Lenstra Jr, L. Lovasz, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.

    B. Just, Generalizing the continued fraction algorithm to arbitrary dimensions, SIAM J. Comput. 21 (1992), 909-926.


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