[University
of Oulu] [Faculty of
Science] [Department of Mathematical
Sciences]
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Professor
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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.
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. 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). 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. |