Carsten Elsner

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All published works

Action	Title	Year	Authors
+ PDF Chat	On algebraic conditions for the non-vanishing of linear forms in Jacobi theta-constants	2024	Carsten Elsner Varun Kumar
+	Diophantine Analysis Around $$[1,2,3,\dots ]$$	2023	Carsten Elsner Christopher Havens
+	On a criterion for algebraic independence and its variants	2023	Gessica Alecci Carsten Elsner
+	A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers	2022	Daniel Duverney Carsten Elsner Masanobu Kaneko Yohei Tachiya
+	Algebraic independence results for the values of the theta-constants and some identities	2020	Carsten Elsner Masanobu Kaneko Yohei Tachiya
+ PDF Chat	ON LINEAR RELATIONS FOR DIRICHLET SERIES FORMED BY RECURSIVE SEQUENCES OF SECOND ORDER	2020	Carsten Elsner Niclas Technau
+	On Linear Independence Results for Values of Jacobi Theta-Constants	2019	Carsten Elsner Veekesh Kumar
+	On Linear Forms in Jacobi theta-constants	2019	Carsten Elsner Veekesh Kumar
+	The Lucas property for linear recurrences of second order	2018	Carsten Elsner Jürgen Spilker
+	Algebraic results for certain values of the Jacobi theta-constant $\theta_3(\tau)$	2018	Carsten Elsner Yohei Tachiya
+ PDF Chat	Algebraic results for the values 𝜗3(mτ) and 𝜗3(nτ) of the Jacobi theta-constant	2018	Carsten Elsner Florian Luca Yohei Tachiya
+	On linear relations for Dirichlet series formed by recursive sequences of second order.	2018	Carsten Elsner Niclas Technau
+	On linear relations for Dirichlet series formed by recursive sequences of second order	2018	Carsten Elsner Niclas Technau
+	Algebraic independence results for values of Theta-constants, II	2016	Carsten Elsner Yohei Tachiya
+	On error sums formed by rational approximations with split denominators	2016	Thomas Baruchel Carsten Elsner
+	Algebraic independence results for values of Jacobi theta-constants	2016	Carsten Elsner Yohei Tachiya
+	On Error Sum Functions for Approximations with Arithmetic Conditions	2016	Carsten Elsner
+	On Reciprocal Sums Formed by Solutions of Pell's Equation.	2016	Carsten Elsner
+ PDF Chat	Algebraic independence results for values of theta-constants	2015	Carsten Elsner
+	ALGEBRAIC INDEPENDENCE OF VALUES OF EXPONENTIAL TYPE POWER SERIES (Analytic Number Theory : Number Theory through Approximation and Asymptotics)	2014	Carsten Elsner Yu. V. Nesterenko Iekata Shiokawa
+	On Error Sums for Square Roots of Positive Integers with Applications to Lucas and Pell Numbers	2014	Carsten Elsner
+	On algebraic relations for Ramanujan’s functions	2012	Carsten Elsner Iekata Shiokawa
+	Expansion of Euler’s constant in terms of Zeta numbers	2012	Carsten Elsner Marc Prévost
+ PDF Chat	Algebraic independence of certain numbers related to modular functions	2012	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	Algebraic relations for reciprocal sums of even terms in Fibonacci numbers	2012	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	A Zeta Function for Juggling Sequences	2012	Carsten Elsner Dominic Klyve Erik R. Tou
+	Der Widerspenstigen Zähmung:	2011	Carsten Elsner Martin Stein
+	Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers	2011	Carsten Elsner Shun Shimomura Iekata Shiokawa Masaaki Amou Masanori Katsurada
+	On Error Sum Functions Formed by Convergents of Real Numbers	2011	Carsten Elsner Martin Stein
+ PDF Chat	Algebraic independence results for reciprocal sums of Fibonacci numbers	2011	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	Series of Error Terms for Rational Approximations of Irrational Numbers	2011	Carsten Elsner
+	Algebraic independence results for the sixteen families of q-series	2010	Carsten Elsner Shun Shimomura Iekata Shiokawa Yohei Tachiya
+	A remark on Nesterenko’s theorem for Ramanujan functions	2010	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	On a generalization of a formula of Ser and applications to the Riemann zeta function and to Dirichlet L-series	2010	Carsten Elsner
+	On convergents formed from Diophantine equations	2009	Carsten Elsner Takao Komatsu Iekata Shiokawa
+	Algebraic relations and asymptotic formulas for Fibonacci reciprocal sums (解析的整数論とその周辺--RIMS研究集会報告集)	2009	Carsten Elsner 俊下村宇賢塩川
+	ALGEBRAIC RELATIONS AND ASYMPTOTIC FORMULAS FOR FIBONACCI RECIPROCAL SUMS (Analytic Number Theory and Related Areas)	2009	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	Algebraic independence results for Ramanujan $q$-series (New Aspects of Analytic Number Theory)	2009	Carsten Elsner Shun Shimomura Iekata Shiokawa
+ PDF Chat	On Rational Approximations to Euler's Constant and to	2009	Carsten Elsner
+	On Rational Approximations to Euler's Constant γ and to γ+log(a/b).	2009	Carsten Elsner
+ PDF Chat	Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values	2009	Carsten Elsner Shun Shimomura Iekata Shiokawa
+	Reciprocal sums of Fibonacci numbers	2008	Carsten Elsner Shun Shimomura Iekata Shiokawa Takao Komatsu
+	A recurrence formula for leaping convergents of non-regular continued fractions	2007	Carsten Elsner Takao Komatsu
+	Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers	2007	Carsten Elsner Shin‐ichi Shimomura Iekata Shiokawa
+ PDF Chat	Algebraic relations for reciprocal sums of Fibonacci numbers	2007	Carsten Elsner Shun Shimomura Iekata Shiokawa
+ PDF Chat	Approximation of values of hypergeometric functions by restricted rationals	2007	Carsten Elsner Takao Komatsu Iekata Shiokawa
+	On a sequence transformation with integral coefficients for Euler's constant, II	2006	Carsten Elsner
+ PDF Chat	On the approximation of real continuous functions by series of solutions of a single system of partial differential equations	2006	Carsten Elsner
+	On Recurrence Formulae for Sums Involving Binomial Coefficients	2005	Carsten Elsner
+	On a method to transform algebraic differential equations into universal equations	2004	Carsten Elsner
+ PDF Chat	H�here Mathematik an der Balkenwaage	2004	Carsten Elsner
+	On a universal differential equation for the analytic terms of C∞-superpositions on the real line	2004	Carsten Elsner
+	On the approximation of continuous functions by analytic solutions of universal functional-differential equations	2004	Carsten Elsner
+	On Rational Approximations by Pythagorean Numbers	2003	Carsten Elsner
+	On a linear transcendence measure for the solutions of a universal differential equation at algebraic points	2003	Carsten Elsner
+	On Inhomogeneous Diophantine Approximations with Rational Terms and Applications to Elliptic and Trigonometric Functions	2002	Carsten Elsner
+	DIOPHANTINE APPROXIMATIONS WITH ARITHMETIC RESTRICTIONS AND AN APPLICATION TO TRIGONOMETRIC FUNCTIONS	2001	Carsten Elsner
+	On Arithmetic Properties of the Solutions of a Universal Differential Equation at Algebraic Points	2001	Carsten Elsner
+	On the distribition of residue classes of quadratic forms and integer-detecting sequences in number fields	2000	Carsten Elsner J. Sander
+	A Universal Differential Equation of Degree 6	2000	Carsten Elsner
+	On Diophantine Approximations with Rational Restricted by Arithmetical Conditions	2000	Carsten Elsner
+	On rational approximations with denominators from thin sets	1999	Carsten Elsner
+ PDF Chat	On arithmetic properties of the convergents of Euler's number	1999	Carsten Elsner
+ PDF Chat	A universal functional equation	1999	Carsten Elsner
+	On the Exact Height of Integer-Detecting Sequences	1998	Carsten Elsner J. Sander
+	A Metric Result Concerning the Approximation of Real Numbers by Continued Fractions	1998	Carsten Elsner
+	On inhomogeneous approximations to irrational numbers with arithmetical conditions	1996	Carsten Elsner
+	On the Approximation of Irrational Numbers with Rationals Restricted by Congruence Relations	1996	Carsten Elsner
+ PDF Chat	On a Sequence Transformation with Integral Coefficients for Euler's Constant	1995	Carsten Elsner
+ PDF Chat	On a sequence transformation with integral coefficients for Euler’s constant	1995	Carsten Elsner
+	On the Approximation of Continuous Functions by C<sup>∞</sup>‐Solutions of Third‐Order Algebraic Differential Equations	1992	Carsten Elsner

Common Coauthors

Coauthor	Papers Together
Iekata Shiokawa	16
Shun Shimomura	11
Yohei Tachiya	7
Takao Komatsu	4
Niclas Technau	3
Masanobu Kaneko	2
Veekesh Kumar	2
J. Sander	2
Martin Stein	2
Masaaki Amou	1
Marc Prévost	1
Thomas Baruchel	1
Masanori Katsurada	1
Varun Kumar	1
Jürgen Spilker	1
Shin‐ichi Shimomura	1
Erik R. Tou	1
Yu. V. Nesterenko	1
Florian Luca	1
宇賢塩川	1
Daniel Duverney	1
俊下村	1
Dominic Klyve	1
Christopher Havens	1
Gessica Alecci	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Modular functions and transcendence questions	1996	Yu. V. Nesterenko	12
+	The Summation of Series of Hyperbolic Functions	1979	I. J. Zucker	10
+	Universal Formulae and Universal Differential Equations	1986	Michael Boshernitzan	9
+ PDF Chat	Algebraic relations for reciprocal sums of Fibonacci numbers	2007	Carsten Elsner Shun Shimomura Iekata Shiokawa	8
+ PDF Chat	Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers	1997	Daniel Duverney Keiji Nishioka Kumiko Nishioka Iekata Shiokawa	7
+ PDF Chat	On rational approximations to irrational numbers	1980	Saburô Uchiyama	7
+ PDF Chat	Модулярные функции и вопросы трансцендентности	1996	Юрий Валентинович Нестеренко Yuri Valentinovich Nesterenko	7
+	A Universal Differential Equation of Degree 6	2000	Carsten Elsner	6
+	On the Approximation of Irrationals by Rationals	1998	Carstenelsner	6
+ PDF Chat	Sur une condition supplémentaire dans les approximations diophantiques	1949	S. Hartman	6
+ PDF Chat	Algebraic independence results for reciprocal sums of Fibonacci numbers	2011	Carsten Elsner Shun Shimomura Iekata Shiokawa	6
+	Handbook of Mathematical Functions	1966	Donald A. McQuarrie	6
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	5
+ PDF Chat	On arithmetic properties of the convergents of Euler's number	1999	Carsten Elsner	5
+	Arithmetical properties of some series with logarithmic coefficients	2006	Khodabakhsh Hessami Pilehrood Tatiana Hessami Pilehrood	5
+ PDF Chat	A universal functional equation	1999	Carsten Elsner	5
+ PDF Chat	Rubel's universal differential equation	1981	R. J. Duffin	4
+ PDF Chat	Algebraic independence results for values of theta-constants	2015	Carsten Elsner	4
+	The solutions to a smooth PDE can be dense in C[I]	1981	R. Creighton Buck	4
+ PDF Chat	Transcendence of Jacobi's theta series	1996	Daniel Duverney Keiji Nishioka Kumiko Nishioka Iekata Shiokawa	4
+	Series of Error Terms for Rational Approximations of Irrational Numbers	2011	Carsten Elsner	4
+	A remark on Nesterenko’s theorem for Ramanujan functions	2010	Carsten Elsner Shun Shimomura Iekata Shiokawa	4
+	Handbook of Elliptic Integrals for Engineers and Physicists	1954	Paul F. Byrd Morris D. Friedman	4
+	None	1997	Daniel Bertrand	4
+	Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers	2007	Carsten Elsner Shin‐ichi Shimomura Iekata Shiokawa	4
+ PDF Chat	On Diophantine approximations	1961	L. C. Eggan	3
+	The error-sum function of continued fractions	2000	J. N. Ridley G. Petruska	3
+ PDF Chat	Arithmetical Properties of the Leaping Convergents of $e^{1/s}$	2004	Takao Komatsu	3
+	On a linear transcendence measure for the solutions of a universal differential equation at algebraic points	2003	Carsten Elsner	3
+ PDF Chat	Euler’s constant to 1271 places	1962	Donald E. Knuth	3
+	On Arithmetic Properties of the Solutions of a Universal Differential Equation at Algebraic Points	2001	Carsten Elsner	3
+	Criteria for irrationality of Euler’s constant	2003	Jonathan Sondow	3
+	Euler's Constant to 1271 Places	1962	Donald E. Knuth	3
+	A Note on the Irrationality of ζ(2) and ζ(3)	1979	Frits Beukers	3
+	A Primer of Real Analytic Functions	1992	Steven G. Krantz Harold R. Parks	3
+ PDF Chat	On a sequence transformation with integral coefficients for Euler’s constant	1995	Carsten Elsner	3
+	On the approximation of continuous functions by analytic solutions of universal functional-differential equations	2004	Carsten Elsner	3
+	On a sequence transformation with integral coefficients for Euler's constant, II	2006	Carsten Elsner	3
+	On algebraic relations for Ramanujan’s functions	2012	Carsten Elsner Iekata Shiokawa	3
+	Uniform Approximation by Rational Functions Which All Satisfy the Same Algebraic Differential Equation	1996	Lee A. Rubel	3
+	Algebraic independence results for the sixteen families of q-series	2010	Carsten Elsner Shun Shimomura Iekata Shiokawa Yohei Tachiya	3
+	Introduction to Algebraic Independence Theory	2001	Yuri Valentinovich Nesterenko Patrice Philippon	3
+ PDF Chat	A Primer of Real Analytic Functions	2002	Steven G. Krantz Harold R. Parks	2
+	A Short Proof of the Simple Continued Fraction Expansion of <i>e</i>	2006	Henry Cohn	2
+ PDF Chat	Algebraic independence results for reciprocal sums of Fibonacci and Lucas numbers	2011	Martin Stein Masaaki Amou Masanori Katsurada	2
+	Handbook of Mathematical Functions.	1966	Juliette Florentin Milton Abramowitz Irene A. Stegun	2
+	Introduction to number theory	2009	Luo Hua	2
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	2
+ PDF Chat	A family of criteria for irrationality of Euler's constant	2008	Marc Prévost	2
+ PDF Chat	Rational approximations for values of derivatives of the Gamma function	2009	Tanguy Rivoal	2