Arithmetical results on some infinite products. (English) Zbl 1479.11128
Reviewer: Jaroslav Hančl (Ostrava)
Found 77 Documents (Results 1–77)
On simultaneous approximation of the values of certain Mahler functions. (English) Zbl 1465.11169
Reviewer: Jan Šustek (Ostrava)
Note on the Stern-Brocot sequence, some relatives, and their generating power series. (English. French summary) Zbl 1428.11132
Reviewer: Michel Waldschmidt (Paris)
An application of Mahler’s method to continued fractions. (English) Zbl 1413.11087
Reviewer: Jaroslav Hančl (Ostrava)
Hypertranscendence and algebraic independence of certain infinite products. (English) Zbl 1410.11101
Algebraic independence of certain Mahler functions. (English) Zbl 1404.11098
Reviewer: Jürgen Wolfart (Frankfurt am Main)
Padé approximations of a class of G-functions and some applications. arXiv:1807.10011
Preprint, arXiv:1807.10011 [math.NT] (2018).
Guided by Schwarz’ functions: a walk through the garden of Mahler’s transcendence method. (English) Zbl 1407.11090
Sander, Jürgen (ed.) et al., From arithmetic to zeta-functions. Number theory in memory of Wolfgang Schwarz. Cham: Springer. 91-101 (2016).
Algebraic independence of certain Mahler numbers. (English) Zbl 1353.11084
Reviewer: Takao Komatsu (Wuhan)
Arithmetic properties of infinite products of cyclotomic polynomials. (English) Zbl 1341.11042
Reviewer: Jürgen Wolfart (Frankfurt am Main)
Algebraic independence results on the generating Lambert series of the powers of a fixed integer. (English) Zbl 1378.11078
Reviewer: Michel Waldschmidt (Paris)
Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers. (English) Zbl 1395.11110
Reviewer: Takao Komatsu (Wuhan)
Algebraic independence of the generating functions of the stern polynomials and their twisted analogues. (English) Zbl 1323.11053
Reviewer: Jaroslav Hančl (Ostrava)
Algebraic independence of certain Mahler functions and of their values. (English) Zbl 1356.11044
Reviewer: Jürgen Wolfart (Frankfurt am Main)
Arithmetical properties of certain infinite products. (English) Zbl 1317.11077
Reviewer: Jürgen Wolfart (Frankfurt am Main)
On certain Mahler functions. (English) Zbl 1349.11106
Reviewer: Robert F. Tichy (Graz)
On rational approximations of certain Mahler functions with a connection to the Thue-Morse sequence. (English) Zbl 1311.11072
Reviewer: Peter Bundschuh (Köln)
MSC:
11J82
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. II. (English) Zbl 1379.11070
Transcendence results on the generating functions of the characteristic functions of certain self-generating sets. (English) Zbl 1292.11082
Reviewer: Jaroslav Hančl (Ostrava)
Algebraic independence of reciprocal sums of certain Fibonacci-type numbers. arXiv:1403.5510
Preprint, arXiv:1403.5510 [math.NT] (2014).
Algebraic independence of the generating functions of Stern’s sequence and of its twist. (English) Zbl 1268.11096
Reviewer: Michel Waldschmidt (Paris)
On Tschakaloff, \(q\)-exponential and related functions. (English) Zbl 1264.11061
Reviewer: Peter Bundschuh (Köln)
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).
Quantitative linear independence of an infinite product and its derivatives. (English) Zbl 1181.11045
Reviewer: Tatiana Hessami Pilehrood (Shahrekord)
On the non-quadraticity of values of the \(q\)-exponential function and related \(q\)-series. (English) Zbl 1232.11080
Reviewer: Peter Bundschuh (Köln)
Linear independence of values of Tschakaloff functions with different parameters. (English) Zbl 1173.11044
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)
On Siegel–Shidlovskii’s theory for \(q\)-difference equations. (English) Zbl 1113.11042
Reviewer: Jaroslav Hančl (Ostrava)
On the values of Heine series at algebraic points. (English) Zbl 1206.11089
Reviewer: Rolf Wallisser (Freiburg i. Br.)
A linear independence measure for the values of Tschakaloff function and an application. (English) Zbl 1173.11337
New irrationality measures for \(q\)-logarithms. (English) Zbl 1158.11033
Reviewer: Peter Bundschuh (Köln)
Linear independence of certain Lambert and allied series. (English) Zbl 1228.11106
Reviewer: Rolf Wallisser (Freiburg i. Br.)
Baker-type estimates for linear forms in the values of \(q\)-series. (English) Zbl 1064.11054
Reviewer: Peter Bundschuh (Köln)
MSC:
11J82
On linear independence of the values of generalized Heine series. (English) Zbl 1025.11023
Reviewer: R.Wallisser (Freiburg i.Br.)
Arithmetic properties of solutions of certain functional equations in several variables. (English) Zbl 1025.11024
Reviewer: R.Wallisser (Freiburg i.Br.)
On the values of certain \(q\)-hypergeometric series. II. (English) Zbl 1027.11048
Jia, Chaohua (ed.) et al., Analytic number theory. Proceedings of the 1st China-Japan seminar on number theory, Beijing, China, September 13-17, 1999 and the annual conference on analytic number theory, Kyoto, Japan, November 29-December 3, 1999. Dordrecht: Kluwer Academic Publishers. Dev. Math. 6, 17-25 (2002).
Reviewer: Peter Bundschuh (Köln)
Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré. (English) Zbl 0984.11037
Reviewer: Peter Bundschuh (Köln)
Linear independence measures for infinite products. (English) Zbl 0999.11036
Reviewer: Takao Komatsu (Tsu)
On the values of certain \(q\)-hypergeometric series. (English) Zbl 1017.11039
Jutila, Matti (ed.) et al., Number theory. Proceedings of the Turku symposium on number theory in memory of Kustaa Inkeri, Turku, Finland, May 31-June 4, 1999. Berlin: de Gruyter, 5-17 (2001).
Reviewer: John H.Loxton (North Ryde)
On the simultaneous diophantine approximation of new products. (English) Zbl 0966.11030
Reviewer: John H.Loxton (North Ryde)
On approximation measures of \(q\)-logarithms. (English) Zbl 0930.11053
Reviewer: P.Bundschuh (Köln)
Transcendental numbers and complex differential equations. (English) Zbl 0873.11045
Laine, Ilpo (ed.), Value distribution theory and complex differential equations. Papers from the workshop, Joensuu, Finland, September 18-21, 1994. Joensuu: University of Joensuu. Publ. Sci., Univ. Joensuu. 35, 45-60 (1995).
Reviewer: T.Komatsu (Nagaoka)
An application of Jacobi type polynomials to irrationality measures. (English) Zbl 0821.11037
Reviewer: Xu Guangshan (Beijing)
Arithmetical investigations of a certain infinite product. (English) Zbl 0802.11027
Reviewer: M.Waldschmidt (Paris)
On the approximation of certain infinite products. (English) Zbl 0818.11028
Reviewer: R.Wallisser (Freiburg i.Br.)
On irrationality measures on the values of Gauss hypergeometric function. (English) Zbl 0801.11032
Reviewer: P.Bundschuh (Köln)
A linear independence measure for certain \(p\)-adic numbers. (English) Zbl 0747.11030
Reviewer: P.Philippon (Paris)
On irrationality measures of certain \(P\)-adic numbers. (English) Zbl 0714.11041
Acta Universitatis Ouluensis. Series A. Scientiae Rerum Naturalium 207. Oulu: Oulu University Press. 16 p. (1989).
Reviewer: Guangshan Xu
MSC:
11J82
Application of Hermite-Mahler polynomials to the approximation of the values of p-adic exponential function. (English) Zbl 0713.11040
Reviewer: K.Väänänen
On the arithmetic properties of the values of G-functions. (English) Zbl 0691.10027
Reviewer: P.Philippon
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
Reviewer: P.Bundschuh
On linear forms of G-functions. (English) Zbl 0654.10034
Reviewer: Frits Beukers (Utrecht)
MSC:
11J91
On linear forms of G-functions. (English) Zbl 0669.10059
MSC:
11J81
On a class of G-functions. (English) Zbl 0542.10030
Théorie des nombres, Sémin. Delange-Pisot-Poitou, Paris 1981/82, Prog. Math. 38, 313-319 (1983).
Remarks on the arithmetic properties of the values of hypergeometric functions. (English) Zbl 0527.10032
MSC:
11J81
On a class of G-functions. (English) Zbl 0542.10029
Mathematics No. 1. Oulu, Finland: University of Oulu, Faculty of Science, Department of Mathematics. 22 p. (1981).
Reviewer: G.Xu
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).
On transcendental numbers. (Finnish) Zbl 0442.10022
On linear forms of a certain class of G-functions and \(p\)-adic G-functions. (English) Zbl 0369.10021
MSC:
11J81
On the arithmetic properties of certain values of the exponential function. (English) Zbl 0431.10020
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
On lower estimates for linear forms involving certain transcendental numbers. (English) Zbl 0317.10043
MSC:
11J81
On the algebraic independence of the values of some E-functions related to Kummer’s functions. (English) Zbl 0315.10029
MSC:
11J81
On the algebraic independence of the values of some E-functions. (English) Zbl 0315.10028
MSC:
11J81
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
On the transcendence and algebraic independence of the values of certain E-functions. (English) Zbl 0266.10031
MSC:
11J81
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