[University of Oulu]  [Faculty of Science]  [Department of Mathematical Sciences]

 

Logo of University of Oulu

Professor
Keijo Väänänen

 

 

LIST OF PUBLICATIONS

1. Väänänen, K. On a conjecture of Mahler concerning the algebraic independence of the values of certain E-functions, Ann. Acad. Sci. Fenn. Ser. A I, 512 (1972), 46 pp.

2. Väänänen, K. The transcendence and algebraic independence of the values of certain E-functions, Acta Univ. Oulu, Ser. A, Math. No. 2 (1973), 13 pp.

3. Väänänen, K. Estimates of the conjugate transcendence measure for the values of some E-functions, Ann. Acad. Sci. Fenn. Ser. A I, 536 (1973), 12 pp.

4. Väänänen, K. On the transcendence and algebraic independence of the values of certain E-functions, Ann. Acad. Sci. Fenn. Ser. A I, 537 1973), 15 pp.

5. Väänänen, K. On the algebraic independence of the values of some E-functions, Ann. Acad. Sci. Fenn. Ser. A I, Vol. 1 (1975), 93-109.

6. Väänänen, K. On the algebraic independence of the values of some E-functions related to Kummer’s functions, Ann. Acad. Sci. Fenn. Ser. A I, Vol. 1 (1975), 183-191.

7. Väänänen, K. On lower estimates for linear forms involving certain transcendental numbers, Bull. Austral. Math. Soc. 14 (1976), 161-179.

8. Väänänen, K. On linear forms of the values of one class of E-functions, Acta Univ. Oulu, Ser. A, Math. No. 12 (1976), 19 pp.

9. Väänänen, K. On lower bounds for polynomials in the values of E-functions, manuscripta math. 21 (1977), 173-180.

10. Väänänen, K. On the simultaneous approximation of certain numbers, J. reine angew. Math. 296 (1977), 205-211.

11. Väänänen, K. On the diophantine approximations of certain numbers related to the exponential function, Mathematics, University of Oulu, No. 20 (1978), 10 pp.

12. Väänänen, K. On the arithmetic properties of certain values of the exponential function, Studia Sci. Math. Hungarica 11 (1976), 399-405.

13. Väänänen, K. On linear forms of a certain class of G-functions and p-adic G-functions, Acta Arith. 36 (1980), 273-295.

14. Väänänen, K. Transkendenttiluvuista, Arkhimedes, 32. vsk. (1980), 165-170.

15. Väänänen, K. On the arithmetic properties of the values of p-adic G-functions, Archiv der Math., Vol. 35 (1980), 364-373.

16. T. Matala-aho and K. Väänänen, On the arithmetic properties of certain values of one Gauss hypergeometric function, Acta Univ. Oulu, Ser. A, Math. No. 24 (1981), 26 pp.

17. K. Väänänen, On a class of G-functions, Mathematics, University of Oulu No. 1/81 (1981), 22 pp.

18. K. Väänänen, On a class of G-functions, Theorie des Nombres, Semin. Delange-Pisot-Poitou, Paris 1981/82, Prog. Math. 38 (1983), 313-319.

19. F. Beukers, T. Matala-aho and K. Väänänen, Remarks on the arithmetic properties of the values of hypergeometric functions, Acta Arith. 42 (1983), 281-289.

20. P. Bundschuh, K. Väänänen, On lower bounds for polynomials in the values of E-functions II, Colloquia Mathematica Societatis Janos Bolyai 34. Topics in classical number theory, Budapest (Hungary), 1981, 229-255.

21. K. Väänänen and Xu Guangshan, On linear forms of G-functions, Kexue Tongbao, Vol. 32, No. 9 (1987), 637-638.

22. K. Väänänen and Xu Guangshan, On linear forms of G-functions, Acta Arith. 50 (1988), 251-263.

23. K. Väänänen and Xu Guangshan, On the arithmetic properties of the values of G-functions, J. Austral. Math. Soc., Ser. A, 47 (1989), 71-82.

24. K. Väänänen, On irrationality of the values of G-functions, Mathematics, University of Oulu, March1989,12 pp.

25. M. Kuukasjärvi, T. Matala-aho and K. Väänänen, On irrationality measures of certain p-adic numbers, Acta Univ. Oul. A 207 (1989), 16 pp.

26. K. Väänänen, Application of Hermite-Mahler polynomials to the approximation of the values of p-adic exponential function, Mh. Math. 108 (1989), 219-227.

27. K. Väänänen, R. Wallisser, Zu einem Satz von Skolem uber lineare Unabhängigkeit von Werten gewisser Thetareihen, manuscripta math. 65 (1989), 199-212.

28. K. Väänänen, R. Wallisser, A linear independence measure for certain p-adic numbers, J. of Number Theory 39 (1991), 225-236.

29. K. Väänänen, A linear independence measure for the values of Tschakaloff function at algebraic points, Mathematics, University of Oulu, February 1993, 10 pp.

30. A. Heimonen, T Matala-aho and K. Väänänen, On irrationality measures of the values of Gauss hypergeometric function, manuscripta math. 81 (1993), 183-202.

31. K. Väänänen, On the approximation of certain infinite products, Math. Scand. 73 (1993), 197-208.

32. P. Bundschuh and K. Väänänen, Arithmetical investigations of a certain infinite product, Compositio Mathematica 91 (1994), 175-199.

33. A. Heimonen, T. Matala-aho and K. Väänänen, An application of Jacobi type polynomials to irrationality measures, Bull. Austral. Math. Soc. Vol. 50 (1994), 225-243.

34. K. Väänänen, Transcendental numbers and complex differential equations, in Value distribution theory and complex differential equations, Joensuu 1994, Ed. Ilpo Laine, University of Joensuu, Publ. in Sciences 35 (1995), 45-60.

35. K. Väänänen, On series of resiprocals of Lucas sequences, Mathematics, University of Oulu, September1997, 8 pp.

36. Tapani Matala-aho and Keijo Väänänen, On approximation measures of q-logarithms, Bull. Austral. Math. Soc. Vol. 58 (1998), 15-31.

37. M.J. Moisio and K.O. Väänänen, Two recursive algorithms for computing the weight distribution of certain irreducible cyclic codes, IEEE Trans. Inform. Theory, Vol. 45, No. 4 (1999), 1244-1249.

38. M. Moisio and K. Väänänen, The number of solutions of certain Catalan equations over finite fields, Mathematics, University of Oulu, May 1999, 8 pp.

39. M. Amou, M. Katsurada, and K. Väänänen, Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré, Colloque Franco-Japonais Théorie des nombres transcendants, Seminar on mathematical sciences, No. 27 (1999), 111-122.

40. Tapani Matala-aho and Keijo Väänänen, On diophantine approximations of Mock theta functions of third order, THE RAMANUJAN JOURNAL 4 (2000), 13-28.


41. P. Bundschuh and K. Väänänen, On the simultaneous diophantine approximations of new products, Analysis 20 (2000), 387-393.

42. M. Amou, M. Katsurada, and K. Väänänen, Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré, Acta Arith. XCIX. 4 (2001), 389-407.

43. M. Amou, M. Katsurada, and K. Väänänen, On the values of certain q-hypergeometric series, in Number Theory "Proceedings of the Turku Symposium on Number Theory in memory of Kustaa Inkeri", Matti Jutila and Tauno Metsänkylä (Eds.), Walter de Gryuter, Berlin, New York (2001), 5-17.

44. P. Bundschuh and K. Väänänen, Linear independence measures for infinite products, manuscripta math. 105 (2001), 253-263.

45. M. Amou, M. Katsurada, and K. Väänänen, On the values of certain q- hypergeometric series II, in "Analytic Number Theory, the joint Proceedings of the China-Japan Number Theory Conference", C. Jia and K. Matsumoto (Eds.), Kluwer, Dordrecht, (2002), 17-25.

46. K. Väänänen, On linear independence of the values of generalized Heine series, Math. Ann. 325 (2003), 123-136;(doi 10.1007/s00208-002-0375-y).

47. M. Amou and K. Väänänen, An analogue of Shidlovskii´s lemma for certain q-difference equations, Aequationes Math. 65 (2003), 93-101; (doi: 0001-9054/03/010093-9).

48. M. Amou and K. Väänänen, Arithmetic properties of solutions of certain functional equations in several variables, J. of Number Theory 96 (2002), 89-104; (doi:10.1006/jnth.2002.2784).

49. M. Moisio and K. Väänänen, A comparision of the number of rational places of certain function fields to the Hasse-Weil bounds, Appl. Algebra Engrg. Comm. Comput., vol. 14, No.5 (2004), 341 - 359; (doi: 10.1007/s 00200-003-0143-3).

50. M. Amou and K. Väänänen, Linear independence of the values of q-hypergeometric series and related functions, THE RAMANUJAN JOURNAL, 9 (3) 2005, 317-339.

51. K. Väänänen and W. Zudilin, Baker-type estimates for linear forms in the values of q-series, Canad. Math. Bull. Vol 48 (1)(2005), 147-160.

52. M. Amou and K. Väänänen, On linear independence of theta values, Monatsh. Math. 144 (2005), 1-11; (doi: 10.1007/s00605-004-0249-0).

53. T. Matala-aho, K. Väänänen and W. Zudilin, New irrationality measures for q-logarithms, Mathematics of Computation, Vol 75, Number 254 (2006), 879-889; (S 0025-5718(05)01812-0).

54. M. Moisio, M. Rinta-aho and K. Väänänen, New deterministic algorithm for constructing normal bases in finite fields, Mathematics, Proceedings of the Algorithmic Information Theory Conference, Vaasan yliopiston julkaisuja 124, (2005), 117-128.

55. Peter Bundschuh and Keijo Väänänen, Linear independence of q-analogues of certain classical constants, Results in Math. 47 (2005), 33-44; (doi 10.1007/s00025-005-0154-4).

56. Peter Bundschuh and Keijo Väänänen, Linear independence of certain Lambert and allied series, Acta Arith. 120.2 (2005), 197-209.

57. L. Koivula, O. Sankilampi and K. Väänänen, A linear independence measure for the values of Tschakaloff function and an application, JP Jour. Algebra, Number Theory & Appl. 6 (1) (2006), 85-101.

58. Olli Sankilampi and Keijo Väänänen, On the values of Heine series at algebraic points, Result. Math. 50 (2007), 141-153; (DOI 10.1007/s00025-006-0240-2).

59. Masaaki Amou, Tapani Matala-aho and Keijo Väänänen, On Siegel-Shidlovskii's theory for q-difference equations, Acta Arith. 127.4 (2007), 309-335.

60. M. Moisio, M, Rinta-aho and K. Väänänen, On the weight distributions of the duals of certain irreducible cyclic codes and hyper-Kloosteman codes, Mathematics, University of Oulu, Preprint, September 2006, 17 pp.

61. K. Väänänen and V.V. Zudilin, Linear independence of values of Tschakaloff series, Uspekhi Mat. Nauk, Vol. 62, No.1 (2007), 197-198 (Russian).

62. Keijo Väänänen and Wadim Zudilin, Linear independence of values of Tschakaloff functions with different parameters, Journal of Number Theory 128 (2008), 2549-2558; (doi: 10.1016/j.jnt.2008.03.003).

63. Remarks on linear independence of certain q-series, Mathematics, University of Oulu, Preprint, May 2007, 6 pp.

64. Peter Bundschuh and Keijo Väänänen, Arithmetical results on certain q-series, II, International Journal of Number Theory, to appear.

65. K. Kononen, M. Moisio, M. Rinta-aho and K. Väänänen, Irreducible polynomials with prescribed trace and restricted norm, JP Journal of Algebra, Number Theory and Applications, Vol. 11 (2) (2008), 223-248.

66. Keijo Väänänen, On arithmetic properties of q-series, Submitted.

67. Christian Krattenthaler, Igor Rochev, Keijo Väänänen and Wadim Zudilin, On the non-quadraticity of values of the q-exponential function and related q-series, Acta Arith. 136.3 (2009), 243-269.

68. Peter Bundschuh and Keijo Väänänen, Quantitative linear independence of an infinite product and its derivatives, manuscripta math., to appear.

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