Keijo Väänänen

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All published works

Action	Title	Year	Authors
+	Arithmetical results on some infinite products	2020	Peter Bundschuh Keijo Väänänen
+ PDF Chat	On simultaneous approximation of the values of certain Mahler functions	2018	Keijo Väänänen Wen Wu
+	Pad\'e approximations of a class of G-functions and some applications.	2018	Keijo Väänänen
+ PDF Chat	On linear independence measures of the values of Mahler functions	2018	Keijo Väänänen Wen Wu
+ PDF Chat	Algebraic independence of certain Mahler functions	2018	Masaaki Amou Keijo Väänänen
+ PDF Chat	On Padé approximations and global relations of some Euler-type series	2018	Keijo Väänänen
+ PDF Chat	Hypertranscendence and algebraic independence of certain infinite products	2018	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Note on the Stern-Brocot sequence, some relatives, and their generating power series	2018	Peter Bundschuh Keijo Väänänen
+	Padé approximations of a class of G-functions and some applications	2018	Keijo Väänänen
+ PDF Chat	On a result of Fel’dman on linear forms in the values of some E-functions	2017	Keijo Väänänen
+	On Pad\'e approximations and global relations of some Euler-type series	2017	Keijo Väänänen
+	On a result of Fel'dman on linear forms in the values of some E-functions	2017	Keijo Väänänen
+	On a result of Fel'dman on linear forms in the values of some E-functions	2017	Keijo Väänänen
+	On Padé approximations and global relations of some Euler-type series	2017	Keijo Väänänen
+ PDF Chat	On algebraic independence of a class of infinite products	2016	Masaaki Amou Keijo Väänänen
+ PDF Chat	Algebraic independence of certain Mahler numbers	2016	Keijo Väänänen
+	ARITHMETIC PROPERTIES OF INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS	2016	Peter Bundschuh Keijo Väänänen
+	On linear independence measures of the values of Mahler functions	2016	Keijo Väänänen Wen Wu
+	Guided by Schwarz’ Functions: A Walk Through the Garden of Mahler’s Transcendence Method	2016	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers	2015	Peter Bundschuh Keijo Väänänen
+	Algebraic independence of the generating functions of the Stern polynomials and their twisted analogues	2015	Peter Bundschuh Keijo Väänänen
+	Algebraic independence of certain Mahler numbers	2015	Keijo Väänänen
+	Arithmetical properties of certain infinite products	2015	Masaaki Amou Keijo Väänänen
+	On simultaneous approximation of the values of certain Mahler functions	2015	Keijo Väänänen Wen Wu
+ PDF Chat	Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II	2015	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Algebraic independence results on the generating Lambert series of the powers of a fixed integer	2015	Peter Bundschuh Keijo Väänänen
+	Algebraic independence of certain Mahler numbers	2015	Keijo Väänänen
+ PDF Chat	ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES	2014	Peter Bundschuh Keijo Väänänen
+	On certain Mahler functions	2014	Peter Bundschuh Keijo Väänänen
+	On rational approximations of certain Mahler functions with a connection to the Thue–Morse sequence	2014	Keijo Väänänen
+	Irrationality Measures of Numbers Related to Some $q$-Basic Hypergeometric Series	2014	Keijo Väänänen
+	Algebraic independence of reciprocal sums of certain Fibonacci-type numbers	2014	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Transcendence results on the generating functions of the characteristic functions of certain self-generating sets	2014	Peter Bundschuh Keijo Väänänen
+	Algebraic independence of reciprocal sums of certain Fibonacci-type numbers	2014	Peter Bundschuh Keijo Väänänen
+	On the values of certain q-hypergeometric series	2013	Masaaki Amou Masanori Katsurada Keijo Väänänen
+ PDF Chat	Algebraic independence of the generating functions of Stern’s sequence and of its twist	2013	Peter Bundschuh Keijo Väänänen
+	On Tschakaloff, q-exponential and related functions	2012	Keijo Väänänen
+ PDF Chat	Remarks on linear independence of certain q-series	2012	Keijo Väänänen
+	AN APPLICATION OF NESTERENKO'S DIMENSION ESTIMATE TO p-ADIC q-SERIES	2011	Peter Bundschuh Keijo Väänänen
+	On the degree of a Kloosterman sum as an algebraic integer	2011	Keijo Kononen Marko Rinta-aho Keijo Väänänen
+	On Integer Values of Kloosterman Sums	2010	Keijo Kononen Marko Rinta-aho Keijo Väänänen
+ PDF Chat	Linear Independence of -Logarithms over the Eisenstein Integers	2010	Peter Bundschuh Keijo Väänänen
+	ARITHMETICAL RESULTS ON CERTAIN q-SERIES, II	2009	Peter Bundschuh Keijo Väänänen
+	On arithmetic properties of q-series (Analytic Number Theory and Related Areas)	2009	Keijo Väänänen
+	On arithmetic properties of q-series (解析的整数論とその周辺--RIMS研究集会報告集)	2009	Keijo Väänänen
+ PDF Chat	On the non-quadraticity of values of the q-exponential function and related q-series	2009	Christian Krattenthaler Igor Rochev Keijo Väänänen Wadim Zudilin
+	Linear independence of values of Tschakaloff functions with different parameters	2008	Keijo Väänänen Wadim Zudilin
+	On the Values of Heine Series at Algebraic Points	2007	Olli Sankilampi Keijo Väänänen
+ PDF Chat	Linear independence of values of Tschakaloff series	2007	Keijo Väänänen Wadim Zudilin
+	Irreducible polynomials with prescribed trace and restricted norm	2007	Keijo Kononen Marko Moisio Marko Rinta-aho Keijo Väänänen
+ PDF Chat	On Siegel–Shidlovskii's theory for q-difference equations	2007	Masaaki Amou Tapani Matala-aho Keijo Väänänen
+	New irrationality measures for 𝑞-logarithms	2005	Tapani Matala-aho Keijo Väänänen Wadim Zudilin
+	Linear Independence of the Values of q-Hypergeometric Series and Related Functions	2005	Masaaki Amou Keijo Väänänen
+	Linear Independence of q-Analogues of Certain Classical Constants	2005	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Baker-Type Estimates for Linear Forms in the Values of <i>q</i>-Series	2005	Keijo Väänänen Wadim Zudilin
+	An analogue of Shidlovskii‚s lemma for certain q-difference equations	2003	Masaaki Amou Keijo Väänänen
+	On linear independence of the values of generalized Heine series	2003	Keijo Väänänen
+	Arithmetic Properties of Solutions of Certain Functional Equations in Several Variables	2002	Masaaki Amou Keijo Väänänen
+	On the Values of Certain q-Hypergeometric Series II	2002	Masaaki Amou Masanori Katsurada Keijo Väänänen
+	Linear independence measures for infinite products	2001	Peter Bundschuh Keijo Väänänen
+ PDF Chat	Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré	2001	Masaaki Amou Masanori Katsurada Keijo Väänänen
+	ON THE SIMULTANEOUS DIOPHANTINE APPROXIMATION OF NEW PRODUCTS	2000	Peter Bundschuh Keijo Väänänen
+ PDF Chat	On approximation measures of <i>q</i>-logarithms	1998	Tapani Matala-aho Keijo Väänänen
+ PDF Chat	An application of Jacobi type polynomials to irrationality measures	1994	Ari Heimonen Tapani Matala-aho Keijo Väänänen
+	Arithmetical investigations of a certain infinite product	1994	Peter Bundschuh Keijo Väänänen
+	On irrationality measures of the values of Gauss hypergeometric function	1993	Ari Heimonen Tapani Matala-aho Keijo Väänänen
+ PDF Chat	On the approximation of certain infinite products.	1993	Keijo Väänänen
+	A linear independence measure for certain p-adic numbers	1991	Keijo Väänänen Rolf Wallisser
+ PDF Chat	On the arithmetic properties of the values of <i>G</i>-functions	1989	Keijo Väänänen Xu Guangshan
+ PDF Chat	On linear forms of G-functions	1988	Keijo Väänänen Xu Guangshan
+ PDF Chat	Remarks on the arithmetic properties of the values of hypergeometric functions	1983	Frits Beukers Keijo Väänänen Tapani Matala-aho
+ PDF Chat	On linear forms of a certain class of G-functions and p-adic G-functions	1980	Keijo Väänänen
+ PDF Chat	On lower estimates for linear forms involving certain transcendental numbers	1976	Keijo Väänänen
+	On the algebraic independence of the values of some E-functions related to Kummer's functions	1975	Keijo Väänänen
+	On the algebraic independence of the values of some E-functions	1975	Keijo Väänänen
+	On a conjecture of Mahler concerning the algebraic independence of the values of some E-functions	1972	Keijo Väänänen

Common Coauthors

Coauthor	Papers Together
Peter Bundschuh	22
Masaaki Amou	10
Tapani Matala-aho	6
Wadim Zudilin	5
Wen Wu	4
Marko Rinta-aho	3
Keijo Kononen	3
Masanori Katsurada	3
Ari Heimonen	2
Xu Guangshan	2
Marko Moisio	1
Igor Rochev	1
Olli Sankilampi	1
Christian Krattenthaler	1
Rolf Wallisser	1
Frits Beukers	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On the algebraic independence of holomorphic solutions of certain functional equations and their values	1977	K. K. Kubota	10
+	Independance lineaire des valeurs des solutions transcendantes de certaines equations fonctionnelles	1988	Jean-Paul Bézivin	9
+	On linear independence of the values of generalized Heine series	2003	Keijo Väänänen	9
+	Arithmetische Eigenschaften spezieller Heinescher Reihen	1984	Thomas Stihl	8
+	Algebraic independence of reciprocal sums of binary recurrences	1997	Kumiko Nishioka	7
+ PDF Chat	On the rational approximation to the Thue–Morse–Mahler numbers	2011	Yann Bugeaud	6
+ PDF Chat	On the rational approximation of the sum of the reciprocals of the Fermat numbers	2012	Michael James Coons	6
+ PDF Chat	Algebraic independence of the generating functions of Stern’s sequence and of its twist	2013	Peter Bundschuh Keijo Väänänen	6
+	Arithmetical investigations of a certain infinite product	1994	Peter Bundschuh Keijo Väänänen	5
+ PDF Chat	Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré	2001	Masaaki Amou Masanori Katsurada Keijo Väänänen	5
+	Hankel Determinants, Padé Approximations, and Irrationality Exponents	2015	Yann Bugeaud Guo-Niu Han Zhi-Ying Wen Jia-Yan Yao	4
+ PDF Chat	Stern polynomials and double-limit continued fractions	2009	Karl Dilcher Kenneth B. Stolarsky	4
+	Algebraic Independence of Sums of Reciprocals of the Fibonacci Numbers	1999	Kumlko Nishioka Taka-aki Tanaka Takeshi Toshimitsu	4
+ PDF Chat	On Siegel–Shidlovskii's theory for q-difference equations	2007	Masaaki Amou Tapani Matala-aho Keijo Väänänen	4
+ PDF Chat	On linear forms of a certain class of G-functions and p-adic G-functions	1980	Keijo Väänänen	4
+	On the irrationality of Σ (1/(qn+r))	1991	Peter Borwein	4
+	Linear independence measures for values of Heine series	1989	Masanori Katsurada	4
+	On the irrationality exponent of the regular paperfolding numbers	2014	Ying-Jun Guo Zhi‐Xiong Wen Wen Wu	4
+	TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF SERIES RELATED TO STERN'S SEQUENCE	2011	Peter Bundschuh	4
+ PDF Chat	Non-converging continued fractions related to the Stern diatomic sequence	2010	Boris Adamczewski	4
+ PDF Chat	On Some Diophantine Inequalities Involving the Exponential Function	1965	A. Baker	4
+	A note on differentially algebraic solutions of first order linear difference equations	1984	Keiji Nishioka	4
+ PDF Chat	Arithmetische Eigenschaften der unendlichen Reihe $$\sum\limits_{v = 0}^\infty {\frac{{x^v }}{{\frac{{v(v - 1)}}{{a2}}}}} $$	1919	Ljubomir Tschakaloff	3
+	Transcendence of certain infinite products	2007	Yohei Tachiya	3
+	ARITHMETICAL RESULTS ON CERTAIN q-SERIES, I	2008	Peter Bundschuh	3
+	Algebraic Independence of Reciprocal Sums of Binary Recurrences II	2002	Kumiko Nishioka	3
+ PDF Chat	Irrationality measures for some automatic real numbers	2009	Boris Adamczewski Tanguy Rivoal	3
+ PDF Chat	ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES	2014	Peter Bundschuh Keijo Väänänen	3
+	Transcendence of Certain Reciprocal Sums of Linear Recurrences	2002	Daniel Duverney Tomoaki Kanoko Taka-aki Tanaka	3
+ PDF Chat	On a paper by A. Baker on the approximation of rational powers of e	1975	Kurt Mahler	3
+ PDF Chat	On the irrationality of certain series	1992	Peter Borwein	3
+	Transcendence of reciprocal sums of binary recurrences	2008	Tomoaki Kanoko Takeshi Kurosawa Iekata Shiokawa	3
+	A measure for the linear independence of certain numbers	1984	Peter Bundschuh Iekata Shiokawa	3
+ PDF Chat	Transcendence of a fast converging series of rational numbers	2001	Daniel Duverney	3
+	Algebraic function solutions of a certain class of functional equations	1985	Keiji Nishioka	3
+	Lower bounds for polynomials in the values of certain entire functions	1996	Wadim Zudilin	3
+ PDF Chat	Propriétés arithmétiques des solutions de certaines équations fonctionnelles de Poincaré	1996	Daniel Duverney	3
+	Legendre type polynomials and irrationality measures.	1990	Masayoshi Hata	3
+ PDF Chat	Extension of Some Theorems of W. Schwarz	2011	Michael James Coons	3
+	ON THE IRRATIONALITY OF THE VALUES OF HYPERGEOMETRIC FUNCTIONS	1986	В. Н. Сорокин	3
+	�ber Potenzreihen mit ganzzahligen Koeffizienten	1921	Fritz Carlson	3
+	Ein Satz �ber ganze Funktionen und Irrationalit�tsaussagen	1970	Peter Bundschuh	3
+	Arithmetical properties of certain infinite products	2015	Masaaki Amou Keijo Väänänen	3
+	Modular functions and transcendence questions	1996	Yu. V. Nesterenko	3
+	THE TRANSCENDENCE OF SERIES RELATED TO STERN'S DIATOMIC SEQUENCE	2010	Michael James Coons	3
+	Arithmetic properties of Euler series	2015	В. Г. Чирский	2
+	Les nombres p-adiques	1975	Yvette Amice	2
+	Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen	1930	Kurt Mahler	2
+ PDF Chat	Lectures on Transcendental Numbers	1976	Kurt Mahler	2
+	A class of hypertranscendental functions	1977	John Loxton A. J. van der Poorten	2