Andrej Dujella:

Diofantske aproksimacije i primjene - Seminarske teme



1. Asimetrične diofantske aproksimacije (Helena Halas, 4.7.2012.)

R. M. Robinson, Unsymmetrical approximation of irrational numbers, Bull. Amer. Math. Soc. 53 (1947), 351–361.

J. Tong, Robinson's theorem on asymmetric Diophantine approximation, Rocky Mountain J. Math. 26 (1996), 329–335.

2. Aproksimacije razlomcima specijalnog tipa (Gorana Aras-Gazić, 12.9.2012.)

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

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

R. M. Robinson, The approximation of irrational numbers by fractions with odd or even terms, Duke Math. J. 7 (1940), 354–359.

3. Lagrangeov i Markovljev spektar

A. M. Rockett, P. Szusz, Continued Fractions, World Scientific, 1992. (Section 4.6)

T.W. Cusick, M.E. Flahive, The Markoff and Lagrange Spectra, American Mathematical Society, 1989.

4. Razvoj u verižni razlomak i transcendentnost broja e (Ivana Božić, 3.10.2012.)

H. Cohn, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly 113 (2006), 57–62.

A. Baker, Transcendental Number Theory, Cambridge University Press, 1990. (Chapter 1)

5. Zarembina slutnja (Ana Barbir, 26.9.2012.)

N. Moshchevitin, On some open problems in Diophantine approximation, preprint, 2012.

H. Niederreiter, Dyadic fractions with small partial quontiens, Monatsh. Math. 101 (1986), 309-315.

6. Mahlerova i Koksmina klasifikacija realnih brojeva (Rozarija Jakšić, 16.10.2013.)

Y. Bugeaud, Approximation by Algebraic Numbers, Cambridge University Press, 2004. (Chapter 3)

A. Baker, Transcendental Number Theory, Cambridge University Press, 1990. (Chapter 8)

7. Primjena diofantskih aproksimacija na problem ruksaka (Tanja Vojković, 11.12.2014.)

A. M. Odlyzko, The rise and fall of knapsack cryptosystems, in: Cryptology and Computational Number Theory, Proceedings of Symposia in Applied Mathematics, Vol. 42, American Mathematical Society, Providence, 1990, 75–88.

J. C. Lagarias, Knapsack public key cryptosystems and Diophantine approximation, in: Advances in Cryptology, Proceedings of Crypto-83, Plenum, New York, 1984, 3–23.

N. P. Smart, The Algorithmic Resolution of Diophantine Equations, Cambridge University Press, 1998. (Section IV.2)

8. NTRU kriptosustav i rešetke (Ana Grozdanić, 9.7.2012.)

J. Hoffstein, N. Howgrave-Graham, J. Pipher, W. Whyte, Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign, in: P. Q. Nguyen, B. Vallee (Eds.): The LLL Algorithm. Survey and Applications, Springer, Berlin, 2010. (Chapter 11)

J. Hoffstein, J. Pipher, J. H. Silverman: An Introduction to Mathematical Cryptography, Springer, 2008. (Sections 6.10, 6.11)

J. Hoffstein, J. Pipher, J.H. Silverman, NTRU: A ring-based public key cryptosystem, Algoritmic Number Theory - ANTS III, LNCS 1423, Springer-Verlag, 1998, pp. 267-288.

D. Coppersmith, A. Shamir, Lattice attacks on NTRU, Advances in Cryptology - EUROCRYPT '97, LNCS 1233, Springer-Verlag, 1997, pp. 52-61.

9. LLL algoritam i faktorizacija polinoma (Sanja Vranić)

J. Klüners, The van Hoeij Algorithm for Factoring Polynomials, in: P. Q. Nguyen, B. Vallee (Eds.): The LLL Algorithm. Survey and Applications, Springer, Berlin, 2010. (Chapter 8)

A. K. Lenstra, H. W. Lenstra, L. Lovász, Factoring polynomials with rational coefficients, Annals of Mathematics 261 (1982), 515-534.

M. van Hoeij, Factoring polynomials and the knapsack problem, Journal of Number Theory 95 (2002), 167-189.

10. Višeparametarske familije Thueovih jednadžbi i Tzanakisova metoda

V. Ziegler, On a certain family of quartic Thue equations with three parameters, Glasnik matematički 41 (2006), 9-30.

B. Jadrijević, A system of Pellian equations and related two-parametric family of quartic Thue equations, Rocky Mountain J. Math. 35 (2005), 547-572.

B. Jadrijević, On two-parametric family of quartic Thue equations, J. Théor. Nombres Bordeaux 17 (2005), 171-177.

11. Separacija korijena cjelobrojnih kubnih polinoma

Y. Bugeaud, M. Mignotte, Polynomial root separation, Intern. J. Number Theory 6 (2010), 587-602.

A. Schönhage, Polynomial root separation examples, J. Symbolic Comput. 41 (2006), 1080-1090.


Andrej Dujella home page