Bundschuh, Peter; Väänänen, Keijo Arithmetical results on some infinite products. (English) Zbl 1479.11128 Funct. Approximatio, Comment. Math. 63, No. 2, 181-188 (2020). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J82 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo; Wu, Wen On simultaneous approximation of the values of certain Mahler functions. (English) Zbl 1465.11169 Math. Z. 292, No. 3-4, 1157-1174 (2019). Reviewer: Jan Šustek (Ostrava) MSC: 11J82 41A21 11J13 11J72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bundschuh, Peter; Väänänen, Keijo Note on the Stern-Brocot sequence, some relatives, and their generating power series. (English. French summary) Zbl 1428.11132 J. Théor. Nombres Bordx. 30, No. 1, 195-202 (2018). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J91 11B37 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo An application of Mahler’s method to continued fractions. (English) Zbl 1413.11087 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 47, 167-172 (2018). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J70 × Cite Format Result Cite Review PDF
Bundschuh, Peter; Väänänen, Keijo Hypertranscendence and algebraic independence of certain infinite products. (English) Zbl 1410.11101 Acta Arith. 184, No. 1, 51-66 (2018). MSC: 11J81 11J91 12H05 34M15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Amou, Masaaki; Väänänen, Keijo Algebraic independence of certain Mahler functions. (English) Zbl 1404.11098 Arch. Math. 111, No. 2, 145-155 (2018). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J85 11J91 39B52 × Cite Format Result Cite Review PDF Full Text: DOI Link
Amou, Masaaki; Väänänen, Keijo On algebraic independence of a class of infinite products. (English) Zbl 1419.11098 J. Number Theory 172, 114-132 (2017). MSC: 11J85 11J91 × Cite Format Result Cite Review PDF Full Text: DOI Link
Väänänen, Keijo Algebraic independence of certain Mahler numbers. (English) Zbl 1353.11084 Int. J. Number Theory 12, No. 8, 2159-2166 (2016). Reviewer: Takao Komatsu (Wuhan) MSC: 11J91 11J81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bundschuh, Peter; Väänänen, Keijo Arithmetic properties of infinite products of cyclotomic polynomials. (English) Zbl 1341.11042 Bull. Aust. Math. Soc. 93, No. 3, 375-387 (2016). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J91 11J81 12H05 11J25 11J87 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Algebraic independence results on the generating Lambert series of the powers of a fixed integer. (English) Zbl 1378.11078 Hardy-Ramanujan J. 38, 36-44 (2016). Reviewer: Michel Waldschmidt (Paris) MSC: 11J91 11J81 39B32 × Cite Format Result Cite Review PDF Full Text: Link
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers. (English) Zbl 1395.11110 Funct. Approximatio, Comment. Math. 53, No. 1, 47-68 (2015). Reviewer: Takao Komatsu (Wuhan) MSC: 11J91 11J81 39B32 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of the generating functions of the stern polynomials and their twisted analogues. (English) Zbl 1323.11053 Arch. Math. 105, No. 2, 139-148 (2015). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J91 11B83 39B32 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of certain Mahler functions and of their values. (English) Zbl 1356.11044 J. Aust. Math. Soc. 98, No. 3, 289-310 (2015). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J91 11J81 11B39 11J85 39B32 × Cite Format Result Cite Review PDF Full Text: DOI
Amou, Masaaki; Väänänen, Keijo Arithmetical properties of certain infinite products. (English) Zbl 1317.11077 J. Number Theory 153, 283-303 (2015). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 11J82 11J81 11J72 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, P.; Väänänen, K. On certain Mahler functions. (English) Zbl 1349.11106 Acta Math. Hung. 145, No. 1, 150-158 (2015). Reviewer: Robert F. Tichy (Graz) MSC: 11J91 11J81 34M15 39B32 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo On rational approximations of certain Mahler functions with a connection to the Thue-Morse sequence. (English) Zbl 1311.11072 Int. J. Number Theory 11, No. 2, 487-493 (2015). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. II. (English) Zbl 1379.11070 Acta Arith. 167, No. 3, 239-249 (2015). MSC: 11J81 11J82 11J91 12F20 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. (English) Zbl 1292.11082 Acta Arith. 162, No. 3, 273-288 (2014). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J82 11J91 30B30 × Cite Format Result Cite Review PDF Full Text: DOI
Rochev, Igor; Väänänen, Keijo On a quantitative form of Bézivin’s method for \(q\)-series. (English) Zbl 1368.11069 Mosc. J. Comb. Number Theory 3, No. 3-4, 169-188 (2013). MSC: 11J82 11J72 × Cite Format Result Cite Review PDF
Bundschuh, Peter; Väänänen, Keijo Algebraic independence of the generating functions of Stern’s sequence and of its twist. (English) Zbl 1268.11096 J. Théor. Nombres Bordx. 25, No. 1, 43-57 (2013). Reviewer: Michel Waldschmidt (Paris) MSC: 11J81 11J82 × Cite Format Result Cite Review PDF Full Text: DOI Numdam
Väänänen, Keijo On Tschakaloff, \(q\)-exponential and related functions. (English) Zbl 1264.11061 Ramanujan J. 30, No. 1, 117-123 (2013). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo Remarks on linear independence of certain \(q\)-series. (English. Russian original) Zbl 1345.11051 J. Math. Sci., New York 180, No. 5, 556-560 (2012); translation from Fundam. Prikl. Mat. 16, No. 5, 41-47 (2010). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Arithmetical results on certain \(q\)-series. IV. (English) Zbl 1337.11045 Mosc. J. Comb. Number Theory 2, No. 2, 3-21 (2012). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF
Bundschuh, Peter; Väänänen, Keijo Arithmetical results on certain \(q\)-series. III. (English) Zbl 1287.11089 Mosc. J. Comb. Number Theory 1, No. 2, 3-26 (2011). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: Link
Bundschuh, Peter; Väänänen, Keijo \(q\)-series: dimension estimates, linear independence. (English) Zbl 1249.11067 Publ. Math. Debr. 79, No. 3-4, 367-378 (2011). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Arithmetical results on certain \(q\)-series. II. (English) Zbl 1290.11107 Int. J. Number Theory 5, No. 7, 1231-1245 (2009). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Quantitative linear independence of an infinite product and its derivatives. (English) Zbl 1181.11045 Manuscr. Math. 129, No. 4, 423-436 (2009). Reviewer: Tatiana Hessami Pilehrood (Shahrekord) MSC: 11J82 11J72 41A21 × Cite Format Result Cite Review PDF Full Text: DOI
Krattenthaler, Christian; Rochev, Igor; Väänänen, Keijo; Zudilin, Wadim On the non-quadraticity of values of the \(q\)-exponential function and related \(q\)-series. (English) Zbl 1232.11080 Acta Arith. 136, No. 3, 243-269 (2009). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J82 11C20 15A15 33D15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Väänänen, Keijo; Zudilin, Wadim Linear independence of values of Tschakaloff functions with different parameters. (English) Zbl 1173.11044 J. Number Theory 128, No. 9, 2549-2558 (2008). MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI Link
Väänänen, K.; Zudilin, V. V. [Zudilin, Wadim] Linear independence of values of Tschakaloff series. (English. Russian original) Zbl 1173.11043 Russ. Math. Surv. 62, No. 1, 196-198 (2007); translation from Usp. Mat. Nauk 62, No. 1, 197-198 (2007). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Amou, Masaaki; Matala-aho, Tapani; Väänänen, Keijo On Siegel–Shidlovskii’s theory for \(q\)-difference equations. (English) Zbl 1113.11042 Acta Arith. 127, No. 4, 309-335 (2007). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J82 11J72 39A13 × Cite Format Result Cite Review PDF Full Text: DOI
Sankilampi, Olli; Väänänen, Keijo On the values of Heine series at algebraic points. (English) Zbl 1206.11089 Result. Math. 50, No. 1-2, 141-153 (2007). Reviewer: Rolf Wallisser (Freiburg i. Br.) MSC: 11J72 11J82 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Koivula, L.; Sankilampi, O.; Väänänen, K. A linear independence measure for the values of Tschakaloff function and an application. (English) Zbl 1173.11337 JP J. Algebra Number Theory Appl. 6, No. 1, 85-101 (2006). MSC: 11J72 11J82 11J13 11J91 × Cite Format Result Cite Review PDF Full Text: Link
Matala-aho, Tapani; Väänänen, Keijo; Zudilin, Wadim New irrationality measures for \(q\)-logarithms. (English) Zbl 1158.11033 Math. Comput. 75, No. 254, 879-889 (2006). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 33D15 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Linear independence of certain Lambert and allied series. (English) Zbl 1228.11106 Acta Arith. 120, No. 2, 197-209 (2005). Reviewer: Rolf Wallisser (Freiburg i. Br.) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo; Zudilin, Wadim Baker-type estimates for linear forms in the values of \(q\)-series. (English) Zbl 1064.11054 Can. Math. Bull. 48, No. 1, 147-160 (2005). Reviewer: Peter Bundschuh (Köln) MSC: 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo On linear independence of the values of generalized Heine series. (English) Zbl 1025.11023 Math. Ann. 325, No. 1, 123-136 (2003). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J82 11J91 11J72 33D15 × Cite Format Result Cite Review PDF Full Text: DOI
Amou, Masaaki; Väänänen, Keijo Arithmetic properties of solutions of certain functional equations in several variables. (English) Zbl 1025.11024 J. Number Theory 96, No. 1, 89-104 (2002). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Amou, Masaaki; Katsurada, Masanori; Väänänen, Keijo Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré. (English) Zbl 0984.11037 Acta Arith. 99, No. 4, 389-407 (2001). Reviewer: Peter Bundschuh (Köln) MSC: 11J72 11J91 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Linear independence measures for infinite products. (English) Zbl 0999.11036 Manuscr. Math. 105, No. 2, 253-263 (2001). Reviewer: Takao Komatsu (Tsu) MSC: 11J72 11J82 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo On the simultaneous diophantine approximation of new products. (English) Zbl 0966.11030 Analysis, München 20, No. 4, 387-393 (2000). Reviewer: John H.Loxton (North Ryde) MSC: 11J82 11J13 × Cite Format Result Cite Review PDF Full Text: DOI
Matala-Aho, Tapani; Väänänen, Keijo On Diophantine approximations of mock theta functions of third order. (English) Zbl 1001.11030 Ramanujan J. 4, No. 1, 13-28 (2000). MSC: 11J82 11J61 11J72 × Cite Format Result Cite Review PDF Full Text: DOI
Matala-Aho, Tapani; Väänänen, Keijo On approximation measures of \(q\)-logarithms. (English) Zbl 0930.11053 Bull. Aust. Math. Soc. 58, No. 1, 15-31 (1998). Reviewer: P.Bundschuh (Köln) MSC: 11J82 11J17 11J61 41A21 × Cite Format Result Cite Review PDF Full Text: DOI
Heimonen, Ari; Matala-aho, Tapani; Väänänen, Keijo An application of Jacobi type polynomials to irrationality measures. (English) Zbl 0821.11037 Bull. Aust. Math. Soc. 50, No. 2, 225-243 (1994). Reviewer: Xu Guangshan (Beijing) MSC: 11J82 11J61 × Cite Format Result Cite Review PDF Full Text: DOI
Bundschuh, Peter; Väänänen, Keijo Arithmetical investigations of a certain infinite product. (English) Zbl 0802.11027 Compos. Math. 91, No. 2, 175-199 (1994). Reviewer: M.Waldschmidt (Paris) MSC: 11J72 11J61 11J82 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Väänänen, K. On the approximation of certain infinite products. (English) Zbl 0818.11028 Math. Scand. 73, No. 2, 197-208 (1993). Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J82 11J72 11J61 11J13 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Heimonen, Ari; Matala-aho, Tapani; Väänänen, Keijo On irrationality measures on the values of Gauss hypergeometric function. (English) Zbl 0801.11032 Manuscr. Math. 81, No. 1-2, 183-202 (1993). Reviewer: P.Bundschuh (Köln) MSC: 11J82 11J61 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, K.; Wallisser, R. A linear independence measure for certain \(p\)-adic numbers. (English) Zbl 0747.11030 J. Number Theory 39, No. 2, 225-236 (1991). Reviewer: P.Philippon (Paris) MSC: 11J72 11J61 11J91 41A21 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, K. Application of Hermite-Mahler polynomials to the approximation of the values of p-adic exponential function. (English) Zbl 0713.11040 Monatsh. Math. 108, No. 2-3, 219-227 (1989). Reviewer: K.Väänänen MSC: 11J81 11J13 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, K.; Xu, Guangshan On the arithmetic properties of the values of G-functions. (English) Zbl 0691.10027 J. Aust. Math. Soc., Ser. A 47, No. 1, 71-82 (1989). Reviewer: P.Philippon MSC: 11J81 11J61 × Cite Format Result Cite Review PDF
Väänänen, K.; Wallisser, R. Zu einem Satz von Skolem über lineare Unabhängigkeiten von Werten gewisser Thetareihen. (On a theorem of Skolem on linear independence of values of certain theta series). (German. English summary) Zbl 0685.10025 Manuscr. Math. 65, No. 2, 199-212 (1989). Reviewer: P.Bundschuh MSC: 11J81 11J61 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, K.; Xu, Guangshan On linear forms of G-functions. (English) Zbl 0654.10034 Acta Arith. 50, No. 3, 251-263 (1988). Reviewer: Frits Beukers (Utrecht) MSC: 11J91 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, K.; Xu, Guangshan On linear forms of G-functions. (English) Zbl 0669.10059 Kexue Tongbao, Sci. Bull. 32, No. 9, 637-638 (1987). MSC: 11J81 × Cite Format Result Cite Review PDF
Beukers, F.; Matala-Aho, T.; Vaeaenaenen, K. Remarks on the arithmetic properties of the values of hypergeometric functions. (English) Zbl 0527.10032 Acta Arith. 42, 281-289 (1983). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Matala-Aho, T.; Vaeaenaenen, K. On the arithmetic properties of certain values of one Gauss hypergeometric function. (English) Zbl 0485.10025 Acta Univ. Oulu., Ser. A 112, Math. 24, 26 p. (1981). MSC: 11J81 11J85 33C60 × Cite Format Result Cite Review PDF
Väänänen, Keijo On transcendental numbers. (Finnish) Zbl 0442.10022 Arkhimedes 32, 165-174 (1980). MSC: 11J81 11-02 × Cite Format Result Cite Review PDF
Väänänen, Keijo On linear forms of a certain class of G-functions and \(p\)-adic G-functions. (English) Zbl 0369.10021 Acta Arith. 36, 273-295 (1980). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, Keijo On lower bounds for polynomials in the values of E-functions. (English) Zbl 0356.10026 Manuscr. Math. 21, 173-180 (1977). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, K. On the simultaneous approximation of certain numbers. (English) Zbl 0356.10025 J. Reine Angew. Math. 296, 205-211 (1977). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Väänänen, K. On the arithmetic properties of certain values of the exponential function. (English) Zbl 0431.10020 Stud. Sci. Math. Hung. 11, 399-405 (1976). MSC: 11J81 11J85 × Cite Format Result Cite Review PDF
Väänänen, Keijo On linear forms of the values of one class of E - functions. (English) Zbl 0329.10025 Acta Univ. Oulu., Ser. A 41, Math. 12, 19 p. (1976). MSC: 11J81 × Cite Format Result Cite Review PDF
Väänänen, Keijo On lower estimates for linear forms involving certain transcendental numbers. (English) Zbl 0317.10043 Bull. Aust. Math. Soc. 14, 161-179 (1976). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo On the algebraic independence of the values of some E-functions related to Kummer’s functions. (English) Zbl 0315.10029 Ann. Acad. Sci. Fenn., Ser. A I, Math. 1, 183-194 (1975). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo On the algebraic independence of the values of some E-functions. (English) Zbl 0315.10028 Ann. Acad. Sci. Fenn., Ser. A I, Math. 1, 93-109 (1975). MSC: 11J81 × Cite Format Result Cite Review PDF Full Text: DOI
Väänänen, Keijo The transcendence and algebraic independence of the values of certain E- functions. (English) Zbl 0285.10025 Acta Univ. Oulu., Ser. A 10, Math. 2, 13 p. (1973). MSC: 11J81 × Cite Format Result Cite Review PDF
Väänänen, Keijo On the transcendence and algebraic independence of the values of certain E-functions. (English) Zbl 0266.10031 Ann. Acad. Sci. Fenn., Ser. A I 537, 15 p. (1973). MSC: 11J81 × Cite Format Result Cite Review PDF
Väänänen, Keijo Estimates of the conjugate transcendence measure for the values of some E-functions. (English) Zbl 0266.10030 Ann. Acad. Sci. Fenn., Ser. A I 536, 12 p. (1973). MSC: 11J81 × Cite Format Result Cite Review PDF
Väänänen, Keijo On a conjecture of Mahler concerning the algebraic independence of the values of some E-functions. (English) Zbl 0238.10021 Ann. Acad. Sci. Fenn., Ser. A I 512, 46 p. (1972). MSC: 11J81 × Cite Format Result Cite Review PDF