## Elsner, Carsten

Compute Distance To:
 Author ID: elsner.carsten Published as: Elsner, Carsten; Elsner, C. External Links: MGP
 Documents Indexed: 77 Publications since 1990, including 1 Book Co-Authors: 19 Co-Authors with 34 Joint Publications 768 Co-Co-Authors
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### Co-Authors

 43 single-authored 16 Shiokawa, Iekata 11 Shimomura, Shun 5 Komatsu, Takao 5 Tachiya, Yohei 3 Sander, Jürgen W. 3 Stein, Martin 2 Kaneko, Masanobu 1 Armknecht, Frederik 1 Duverney, Daniel 1 Klauke, A. 1 Klyve, Dominic 1 Luca, Florian 1 Nesterenko, Yuriĭ Valentinovich 1 Prévost, Marc 1 Schmidt, Martin 1 Spilker, Jürgen 1 Steuding, Jörn 1 Technau, Niclas 1 Tou, Erik R.
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### Serials

 5 Journal of Mathematical Analysis and Applications 5 The Fibonacci Quarterly 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 The Ramanujan Journal 4 Journal of Integer Sequences 3 Studia Scientiarum Mathematicarum Hungarica 3 Journal of Combinatorics and Number Theory 2 Mathematische Semesterberichte 2 Acta Arithmetica 2 Colloquium Mathematicum 2 Functiones et Approximatio. Commentarii Mathematici 2 Journal of Number Theory 2 Mathematische Nachrichten 2 Proceedings of the American Mathematical Society 2 Elemente der Mathematik 2 Linear Algebra and its Applications 2 Journal de Théorie des Nombres de Bordeaux 2 Analysis (München) 2 Integers 2 Moscow Journal of Combinatorics and Number Theory 1 Acta Scientiarum Mathematicarum 1 International Journal of Mathematics and Mathematical Sciences 1 Mathematica Scandinavica 1 Mathematica Slovaca 1 Results in Mathematics 1 Journal of the Ramanujan Mathematical Society 1 Glasnik Matematički. Serija III 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Journal of Mathematical Sciences (New York) 1 Communications on Applied Nonlinear Analysis 1 Journal of the Australian Mathematical Society 1 Šiauliai Mathematical Seminar 1 Research in Number Theory
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### Fields

 65 Number theory (11-XX) 14 Ordinary differential equations (34-XX) 10 Special functions (33-XX) 8 Real functions (26-XX) 7 Approximations and expansions (41-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Numerical analysis (65-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

46 Publications have been cited 145 times in 73 Documents Cited by Year
Algebraic relations for reciprocal sums of Fibonacci numbers. Zbl 1132.11036
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2007
Algebraic independence results for reciprocal sums of Fibonacci numbers. Zbl 1231.11080
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. Zbl 1233.11081
Elsner, C.; Shimomura, S.; Shiokawa, I.
2008
On recurrence formulae for sums involving binomial coefficients. Zbl 1136.40301
Elsner, Carsten
2005
On a sequence transformation with integral coefficients for Euler’s constant. Zbl 0828.65001
Elsner, C.
1995
On arithmetic properties of the convergents of Euler’s number. Zbl 0930.11048
Elsner, C.
1999
Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. Zbl 1345.11011
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
A universal differential equation of degree 6. Zbl 0963.34003
Elsner, C.
2000
A recurrence formula for leaping convergents of non-regular continued fractions. Zbl 1132.05007
Elsner, Carsten; Komatsu, Takao
2008
A universal functional equation. Zbl 0905.34059
Elsner, Carsten
1999
On a sequence transformation with integral coefficients for Euler’s constant. II. Zbl 1169.11056
Elsner, Carsten
2007
On the approximation of continuous functions by analytic solutions of universal functional-differential equations. Zbl 1064.34070
Elsner, C.
2004
A remark on Nesterenko’s theorem for Ramanujan functions. Zbl 1263.11071
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2010
On rational approximations by Pythagorean number. Zbl 1028.11042
Elsner, Carsten
2003
On the approximation of irrationals by rationals. Zbl 0896.11027
Elsner, Carsten
1998
On arithmetic properties of the solutions of a universal differential equation at algebraic points. Zbl 0985.34003
Elsner, Carsten
2001
On an universal functional equation of degree six. Zbl 1022.34057
Elsner, Carsten
2002
On simultaneous approximations of continuous functions by solutions of an algebraic differential equation. Zbl 1017.41015
Elsner, C.
2001
On the residue classes of integer sequences satisfying a linear three term recurrence formula. Zbl 1233.11006
Elsner, Carsten; Komatsu, Takao
2008
On the approximation of irrational numbers with rationals restricted by congruence relations. Zbl 0841.11034
Elsner, C.
1996
On the distribution of residue classes of quadratic forms and integer-detecting sequences in number fields. Zbl 1062.11073
Elsner, C.; Sander, J. W.
2000
On rational approximations with denominators from thin sets. Zbl 0946.11013
Elsner, C.
1999
Algebraic independence results for values of theta-constants. Zbl 1325.11074
Elsner, Carsten
2015
On a linear transcendence measure for the solutions of a universal differential equation at algebraic points. Zbl 1026.34009
Elsner, Carsten
2003
Algebraic independence results for the values of the theta-constants and some identities. Zbl 1440.11135
Elsner, Carsten; Kaneko, Masanobu; Tachiya, Yohei
2020
Expansion of Euler’s constant in terms of zeta numbers. Zbl 1323.11050
Elsner, Carsten; Prévost, Marc
2013
On algebraic relations for Ramanujan’s functions. Zbl 1277.11079
Elsner, Carsten; Shiokawa, Iekata
2012
On the value distribution of error sums for approximations with rational numbers. Zbl 1279.11071
Elsner, Carsten; Stein, Martin
2012
A zeta function for juggling sequences. Zbl 1282.11117
Elsner, Carsten; Klyve, Dominic; Tou, Erik R.
2012
Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. Zbl 1279.11074
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
Algebraic independence results for the sixteen families of $$q$$-series. Zbl 1256.11040
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata; Tachiya, Yohei
2010
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Zbl 1233.11018
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2009
Algebraic independence of certain numbers related to modular functions. Zbl 1290.11109
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
On convergents formed from Diophantine equations. Zbl 1233.11031
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2009
On error sum functions formed by convergents of real numbers. Zbl 1255.11036
Elsner, Carsten; Stein, Martin
2011
Approximation of values of hypergeometric functions by restricted rationals. Zbl 1167.11026
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2007
Algebraic relations for reciprocal sums of binary recurrences. Zbl 1155.11041
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2006
On the approximation of continuous functions by $$C^ \infty$$-solutions of third-order algebraic differential equations. Zbl 0813.34014
Elsner, Carsten
1992
On inhomogeneous approximations to irrational numbers with arithmetical conditions. Zbl 0864.11036
Elsner, C.
1996
On rational approximations with denominators from thin sets. II. Zbl 1101.11023
Elsner, C.
2002
On diophantine approximations with rationals restricted by arithmetical conditions. Zbl 0944.11023
Elsner, Carsten
2000
Algebraic independence of values of exponential type power series. Zbl 1352.11058
Elsner, Carsten; Nesterenko, Yuri V.; Shiokawa, Iekata
2013
Diophantine approximations with arithmetic restrictions and an application to trigonometric functions. Zbl 1013.11033
Elsner, C.
2001
Series of error terms for rational approximations of irrational numbers. Zbl 1248.11049
Elsner, Carsten
2011
Algebraic results for certain values of the Jacobi theta-constant $$\theta_3(\tau)$$. Zbl 1440.11136
Elsner, Carsten; Tachiya, Yohei
2018
On the representation of integers by sums of squares with terms from an arithmetic progression. Zbl 1239.11045
Elsner, C.
2000
Algebraic independence results for the values of the theta-constants and some identities. Zbl 1440.11135
Elsner, Carsten; Kaneko, Masanobu; Tachiya, Yohei
2020
Algebraic results for certain values of the Jacobi theta-constant $$\theta_3(\tau)$$. Zbl 1440.11136
Elsner, Carsten; Tachiya, Yohei
2018
Algebraic independence results for values of theta-constants. Zbl 1325.11074
Elsner, Carsten
2015
Expansion of Euler’s constant in terms of zeta numbers. Zbl 1323.11050
Elsner, Carsten; Prévost, Marc
2013
Algebraic independence of values of exponential type power series. Zbl 1352.11058
Elsner, Carsten; Nesterenko, Yuri V.; Shiokawa, Iekata
2013
Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. Zbl 1345.11011
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
On algebraic relations for Ramanujan’s functions. Zbl 1277.11079
Elsner, Carsten; Shiokawa, Iekata
2012
On the value distribution of error sums for approximations with rational numbers. Zbl 1279.11071
Elsner, Carsten; Stein, Martin
2012
A zeta function for juggling sequences. Zbl 1282.11117
Elsner, Carsten; Klyve, Dominic; Tou, Erik R.
2012
Algebraic independence of certain numbers related to modular functions. Zbl 1290.11109
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2012
Algebraic independence results for reciprocal sums of Fibonacci numbers. Zbl 1231.11080
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. Zbl 1279.11074
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2011
On error sum functions formed by convergents of real numbers. Zbl 1255.11036
Elsner, Carsten; Stein, Martin
2011
Series of error terms for rational approximations of irrational numbers. Zbl 1248.11049
Elsner, Carsten
2011
A remark on Nesterenko’s theorem for Ramanujan functions. Zbl 1263.11071
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2010
Algebraic independence results for the sixteen families of $$q$$-series. Zbl 1256.11040
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata; Tachiya, Yohei
2010
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values. Zbl 1233.11018
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2009
On convergents formed from Diophantine equations. Zbl 1233.11031
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2009
Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. Zbl 1233.11081
Elsner, C.; Shimomura, S.; Shiokawa, I.
2008
A recurrence formula for leaping convergents of non-regular continued fractions. Zbl 1132.05007
Elsner, Carsten; Komatsu, Takao
2008
On the residue classes of integer sequences satisfying a linear three term recurrence formula. Zbl 1233.11006
Elsner, Carsten; Komatsu, Takao
2008
Algebraic relations for reciprocal sums of Fibonacci numbers. Zbl 1132.11036
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2007
On a sequence transformation with integral coefficients for Euler’s constant. II. Zbl 1169.11056
Elsner, Carsten
2007
Approximation of values of hypergeometric functions by restricted rationals. Zbl 1167.11026
Elsner, Carsten; Komatsu, Takao; Shiokawa, Iekata
2007
Algebraic relations for reciprocal sums of binary recurrences. Zbl 1155.11041
Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata
2006
On recurrence formulae for sums involving binomial coefficients. Zbl 1136.40301
Elsner, Carsten
2005
On the approximation of continuous functions by analytic solutions of universal functional-differential equations. Zbl 1064.34070
Elsner, C.
2004
On rational approximations by Pythagorean number. Zbl 1028.11042
Elsner, Carsten
2003
On a linear transcendence measure for the solutions of a universal differential equation at algebraic points. Zbl 1026.34009
Elsner, Carsten
2003
On an universal functional equation of degree six. Zbl 1022.34057
Elsner, Carsten
2002
On rational approximations with denominators from thin sets. II. Zbl 1101.11023
Elsner, C.
2002
On arithmetic properties of the solutions of a universal differential equation at algebraic points. Zbl 0985.34003
Elsner, Carsten
2001
On simultaneous approximations of continuous functions by solutions of an algebraic differential equation. Zbl 1017.41015
Elsner, C.
2001
Diophantine approximations with arithmetic restrictions and an application to trigonometric functions. Zbl 1013.11033
Elsner, C.
2001
A universal differential equation of degree 6. Zbl 0963.34003
Elsner, C.
2000
On the distribution of residue classes of quadratic forms and integer-detecting sequences in number fields. Zbl 1062.11073
Elsner, C.; Sander, J. W.
2000
On diophantine approximations with rationals restricted by arithmetical conditions. Zbl 0944.11023
Elsner, Carsten
2000
On the representation of integers by sums of squares with terms from an arithmetic progression. Zbl 1239.11045
Elsner, C.
2000
On arithmetic properties of the convergents of Euler’s number. Zbl 0930.11048
Elsner, C.
1999
A universal functional equation. Zbl 0905.34059
Elsner, Carsten
1999
On rational approximations with denominators from thin sets. Zbl 0946.11013
Elsner, C.
1999
On the approximation of irrationals by rationals. Zbl 0896.11027
Elsner, Carsten
1998
On the approximation of irrational numbers with rationals restricted by congruence relations. Zbl 0841.11034
Elsner, C.
1996
On inhomogeneous approximations to irrational numbers with arithmetical conditions. Zbl 0864.11036
Elsner, C.
1996
On a sequence transformation with integral coefficients for Euler’s constant. Zbl 0828.65001
Elsner, C.
1995
On the approximation of continuous functions by $$C^ \infty$$-solutions of third-order algebraic differential equations. Zbl 0813.34014
Elsner, Carsten
1992
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### Cited by 62 Authors

 31 Elsner, Carsten 9 Shiokawa, Iekata 7 Chu, Wenchang 6 Komatsu, Takao 6 Shimomura, Shun 5 Tachiya, Yohei 4 Rout, Sudhansu Sekhar 4 Wang, Andrew Y. Z. 3 Meher, Nabin Kumar 2 Dutta, Utkal Keshari 2 Duverney, Daniel 2 Esposito, Flavia Lucia 2 Rasa, Ioan 2 Ray, Prasanta Kumar 2 Sander, Jürgen W. 2 Wang, Xiaoyuan 2 Wu, Zhengang 2 Zhang, Fan 1 Acu, Ana Maria 1 Adell, José Antonio 1 Barbero, Stefano 1 Bascanbaz-Tunca, Gulen 1 Behera, Debismita 1 Bracken, Paul Francis 1 Burger, Edward B. 1 Cangul, Ismail Naci 1 Cerruti, Umberto 1 Çevik, Ahmet Sinan 1 Chaichana, Tuangrat 1 Chistikov, Dmitry V. 1 Cooper, Shaun 1 Das, Kinkar Chandra 1 Goulko, Olga 1 Havens, Christopher 1 Hessami Pilehrood, Khodabakhsh 1 Hessami Pilehrood, Tatiana 1 Kamano, Ken 1 Kaneko, Masanobu 1 Kent, Adrian 1 Kumar, Veekesh 1 Kurosawa, Takeshi 1 Lagarias, Jeffrey C. 1 Laohakosol, Vichian 1 Lekuona, Alberto 1 Liu, Runnan 1 Luca, Florian 1 Murru, Nadir 1 Panda, Gopal Krishna 1 Paterson, Mike S. 1 Pillai, Ashok M. 1 Popa, Dorian 1 Rivoal, Tanguy 1 Simsek, Yilmaz 1 Sîntămărian, Alina 1 Stein, Martin 1 Steinig, John 1 Steuding, Jörn 1 Technau, Niclas 1 Tou, Erik R. 1 Wen, Peibo 1 Zhang, Han 1 Zhang, Wenpeng
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### Cited in 43 Serials

 8 The Ramanujan Journal 5 Journal of Mathematical Analysis and Applications 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Journal of Number Theory 3 Indagationes Mathematicae. New Series 3 Journal of Inequalities and Applications 3 Advances in Difference Equations 2 Functiones et Approximatio. Commentarii Mathematici 2 Proceedings of the Japan Academy. Series A 2 Linear Algebra and its Applications 2 Journal de Théorie des Nombres de Bordeaux 2 Integers 2 Research in Number Theory 1 Indian Journal of Pure & Applied Mathematics 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Mathematische Semesterberichte 1 Mathematics of Computation 1 Archiv der Mathematik 1 International Journal of Mathematics and Mathematical Sciences 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Results in Mathematics 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Numerical Algorithms 1 Elemente der Mathematik 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Mathematical Sciences (New York) 1 Mathematical Inequalities & Applications 1 Analysis (München) 1 Acta et Commentationes Universitatis Tartuensis de Mathematica 1 Journal of the Australian Mathematical Society 1 Mediterranean Journal of Mathematics 1 Fixed Point Theory and Applications 1 International Journal of Number Theory 1 Contributions to Discrete Mathematics 1 Online Journal of Analytic Combinatorics 1 European Journal of Pure and Applied Mathematics 1 Moscow Journal of Combinatorics and Number Theory 1 Journal of Classical Analysis 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Cited in 17 Fields

 64 Number theory (11-XX) 9 Real functions (26-XX) 9 Special functions (33-XX) 6 Ordinary differential equations (34-XX) 5 Sequences, series, summability (40-XX) 3 Functions of a complex variable (30-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 1 Group theory and generalizations (20-XX) 1 General topology (54-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX)