Publizierte Schriften
-
"On Mahler's approximation function for powers of certain
algebraic numbers",
Studia Scientiarum Mathematicarum Hungarica 27
(1992), 147-158.
-
"On the approximation of continuous functions by C(infinity)
-solutions of third order algebraic
differential equations",
Mathematische Nachrichten 157 (1992), 235-241.
-
"On a sequence transformation with integral coefficients for
Euler's constant",
Proceedings of the AMS 123, no.5 (1995),
1537-1541.
-
"On the approximation of irrational numbers with rationals
restricted by congruence relations",
The Fibonacci Quarterly 34, no.1 (1996), 18-29.
-
"On inhomogeneous approximation to irrational numbers with
arithmetical conditions",
Abh.Math.Sem.Univ.Hamburg 66 (1996), 223-228.
-
"On the approximation of irrationals by rationals",
Mathematische Nachrichten 189 (1998), 243-256.
-
"A metric result concerning the approximation of real numbers by
continued fractions",
The Fibonacci Quarterly 36, no.4 (1998),
290-294.
- Mit
J.W.Sander: "On the exact height of integer-detecting
sequences",
Journal of Number Theory 73 (1998), 1-13.
-
"A universal functional equation",
Proceedings of the AMS 127, no. 1 (1999),
139-143.
-
"On arithmetic properties of the convergents of Euler's number",
Colloquium Mathematicum 79, no. 1 (1999),
133-145.
-
"On rational approximations with denominators from thin sets",
Abh.Math.Sem.Univ.Hamburg 69 (1999), 229-235.
-
"On the representation of integers by sums of squares with terms
from an arithmetic progression",
Nieuw Archief voor Wiskunde 17, no. 3
(1999), 331-341.
- "Der Dialog der Schwestern",
c't magazin für computer technik 25 (1999),
288-296.
-
"On diophantine approximations with rationals restricted by
arithmetical conditions",
The Fibonacci Quarterly 38, no.1 (2000), 25-34.
-
"A universal differential equation of degree six",
Journal of Mathematical Analysis and Applications 244
(2000), 533-541.
-
Mit J.W.Sander: "On the distribution of residue classes
of quadratic forms and integer-detecting
sequences in number fields",
Studia Scientiarum Mathematicarum Hungarica 36
(2000), 123-152.
- "Über
eine effektive Konstruktion großer Mengen algebraisch
unabhängiger Zahlen",
Mathematische Semesterberichte 47 (2000),
243-256.
-
"On arithmetic properties of the solutions of a universal
differential equation at algebraic points",
Journal of Mathematical Analysis and Applications 256
(2001), 324-338.
- Mit J.W.Sander und J.Steuding:
"Kettenbrüche
als Summe ebensolcher"
(English
version),
Mathematica Slovaca 51 (2001), no.3, 281-293.
- "Das chinesische Labyrinth",
c't magazin für computer technik 21 (2001),
308-312; (www.heise.de/ct
Rubrik Magazin).
-
"Diophantine
approximations with arithmetic restrictions and an application
to trigonometric functions",
Analysis 21 (2001), 327-337.
-
"On
simultaneous approximations of continuous functions by solutions
of an algebraic differential equation",
Acta Sci.Math.(Szeged)
67 (2001), 697-708.
-
"On
an universal functional equation of degree six"
Applied Nonlinear Analysis 9 (2002) no.3,
23-29.
-
"On
rational approximation with denominators from thin sets, I I
",
Abh.Math.Sem.Univ.Hamburg 72 (2002), 35-45.
-
"On
inhomogeneous diophantine approximations with rational terms and
applications to
elliptic and trigonometric functions",
Resultate der Mathematik 42 (2002), 235-251.
-
"On a linear transcendence
measure for the solutions of a universal differential equation
at algebraic points",
Journal of Mathematical Analysis and Applications
279 (2003), 684-699.
-
"On rational approximations by
Pythagorean numbers",
The Fibonacci Quarterly
41 no.2 (2003), 98-104.
-
"On the approximation of
continuous functions by analytic solutions of universal
functional-differential
equations",
Studia Scientiarum Mathematicarum Hungarica
41 (1) (2004), 1-15.
-
"On a universal differential
equation for the analytic terms of C(infinity) - superpositions
on the real line",
Journal of Mathematical Analysis and Applications
295 (2004), 315-330.
-
"Höhere Mathematik an der
Balkenwaage"
Elemente der Mathematik
59 (2004), 151-170.
-
"On a method to transform
algebraic differential equations into universal equations",
Abh.Math.Sem.Univ.Hamburg
74 (2004),
33-48.
-
"On recurrence formulae for
sums involving binomial coefficients",
The Fibonacci Quarterly
43 no.1 (2005), 31-45.
-
"On
the approximation of real continuous functions by series of
solutions of a single system of partial differential equations",
Colloquium Mathematicum
104 no.1 (2006),
57-84.
-
"Über
gewisse Lösungen universeller Differentialgleichungen in
algebraischen Punkten",
Elementare und Analytische Zahlentheorie,
Proceedings ELAZ-Conference, May 24-28, 2004, Schriften der
Wissenschaftlichen
Gesellschaft 20,
Franz Steiner Verlag (2006), 44-56.
-
"On
a sequence transformation with integral coefficients for Euler’s
constant",
Seminar on Mathematical Sciences: Diophantine Analysis and
Related Fields,
Keio
University,
Yokohama, no.35
(2006), 39-57.
- Mit
T.Komatsu und I.Shiokawa: "On convergents formed by Pythagorean
numbers",
Seminar on Mathematical Sciences: Diophantine Analysis and
Related Fields,
Keio
University,
Yokohama, no.35
(2006), 59-76.
- Mit
S.Shimomura und I.Shiokawa: "Algebraic relations for reciprocal
sums of binary recurrences",
Seminar on Mathematical Sciences: Diophantine Analysis and
Related Fields,
Keio
University,
Yokohama, no.35
(2006), 77-92.
- Mit
S.Shimomura und I.Shiokawa: "Algebraic relations and asymptotic
formulas for Fibonacci reciprocal sums",
Analytic Number Theory and Related Areas, October 17-19 (2007),
edited by K.Kawada, RIMS Kôkyûroku 1665,
Kyoto
University,
Kyoto, 127-138.
-
"On a sequence transformation
with integral coefficients for Euler’s constant, II",
Journal of Number Theory
124
(2007), 442 – 453.
-
Mit S.Shimomura und I.Shiokawa:
"Algebraic
relations for reciprocal sums of Fibonacci numbers",
Acta Arithmetica
130.1
(2007), 37 – 60.
-
Mit T.Komatsu und I.Shiokawa: "Approximation
of values of hypergeometric functions by restricted rationals",
Journal de Théorie des Nombres de Bordeaux
19 (2007), 393 –
404.
-
Mit T.Komatsu:
"A
recurrence formula for leaping convergents of non-regular
continued fractions",
Linear Algebra and its Applications
428
(2008), 824 – 833.
-
Mit T.Komatsu:
"On
the residue classes of integer sequences satisfying a linear
three term recurrence formula",
Linear Algebra and its Applications
429
(2008), 933 – 947.
-
"On
prime-detecting sequences from Apéry’s recurrence formulae for
ζ(3) and
ζ(2)",
Journal of Integer Sequences,
11
(2008), Article
08.5.1;
http://www.cs.uwaterloo.ca/journals/JIS/VOL11/Elsner/elsner7.html
-
Mit S.Shimomura und I.Shiokawa:
"Algebraic
relations for reciprocal sums of odd terms in Fibonacci numbers",
Ramanujan Journal, 17
(2008), 429
–
446.
-
Mit S.Shimomura und I.Shiokawa:
"Reciprocal sums of Fibonacci numbers"
Diophantine Analysis and Related Fields, DARF 2007/2008,
Yokohama 7-9 March 2007, Kyoto 5-7 March 2008, AIP Conference
Proceedings
976,
77-89, Melville, New York (2008), Takao Komatsu (editor).
-
"On
rational approximations to Euler’s constant γ and to
γ + log (a/b)",
International Journal of Mathematics and Mathematical Sciences,
vol.
2009,
Article ID 626489, 22 pages, 2009. doi: 10.1155/2009/626489.
-
Mit
S.Shimomura und I.Shiokawa:
"Asymptotic
representations for Fibonacci reciprocal sums and Euler’s
formulas for Zeta values",
Journal de Théorie des Nombres de Bordeaux, 21 no.1 (2009), 145
– 157.
-
Mit T.Komatsu und I.Shiokawa:
"On
convergents formed from Diophantine equations",
Glasnik Matematicki, 44 no.2 (2009), 267 – 284.
-
Mit
S.Shimomura
und I.Shiokawa:
"A
remark on Nesterenko’s theorem for Ramanujan functions",
Ramanujan Journal, 21, no. 2 (2010), 211 – 221.
-
"Results
around Rubel’s universal differential equation",
New Directions in Value-Distribution Theory of Zeta and
L-functions, Conference Proceedings,
Würzburg Conference, October 6-10, 2008; Rasa Steuding, Jörn
Steuding (Eds.), Shaker-Verlag,
Aachen 2009, 39-55.
-
Mit
S.Shimomura,
I.Shiokawa und Yohei Tachiya:
"Algebraic
independence results for the sixteen families of q - series",
Ramanujan Journal, 22, no. 3 (2010), 315 – 344.
-
"On
a generalization of a formula of Ser and applications to the Riemann Zeta Function and to Dirichlet L-series
",
Analysis 30 (2010), 411-431; DOI 10.1524/anly.2010.1063.
-
"Series
of error terms for rational approximations of irrational numbers",
Journal of Integer Sequences,
14
(2011), Article 11.1.4;
http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Elsner/elsner9.html
-
Mit S.Shimomura und I.Shiokawa:
"Algebraic
independence results for reciprocal sums of Fibonacci numbers",
Acta Arithmetica
148.3
(2011), 205 – 223.
-
Mit F.Armknecht und Martin Schmidt:
"Using
the inhomogeneous simultaneous approximation problem for
cryptographic design
",
Progress in Cryptology – AFRICACRYPT 2011, 4th
International Conference on Cryptology in Africa, Dakar,
Senegal, July 5-7, 2011, A.Nitaj, D.Pointcheval (Eds.), Springer
Verlag 2011, LNCS 6737, 242—259.
-
Mit M.Stein: "On
error sum functions formed by convergents of real numbers",
Journal of Integer Sequences 14 (2011), Article 11.8.6;
http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Elsner2/elsner10.html
-
Mit M.Stein: "Der
Widerspenstigen Zähmung – ein Ausblick auf die Möglichkeiten
universeller Differentialgleichungen",
Mathematische Semesterberichte 58 (2011), 157-183;
DOI 10.1007/s00591-011-0089-7
-
Mit S.Shimomura und I.Shiokawa:
"Exceptional
algebraic relations for reciprocal sums of Fibonacci and Lucas
numbers",
Diophantine Analysis and Related Fields 2011, AIP Conf. Proc.,
no. 1385, M.Amou and M.Katsurada (Eds.), A.I.P., 2011, 17-31.
-
Mit S.Shimomura und I.Shiokawa:
"Algebraic
relations for reciprocal sums of even terms in Fibonacci numbers",
Journal of Mathematical Sciences,
180,
no. 5 (2012), 650-671;
DOI: 10.1007/s10958-012-0663-0
Translated from: Fundamentalnaya I Prikladnaya Matematika
16,
no. 5 (2010), 173-200.
-
Mit M.Prévost: "Expansion
of Euler’s constant in terms of Zeta numbers",
Journal of Mathematical Analysis and Applications
398,
no. 2 (2013), 508-526;
DOI: 10.1016/j.jmaa.2012.08.065
-
Mit I.Shiokawa: "On
algebraic relations for Ramanujan’s functions",
Ramanujan Journal,
29
(2012), 273-294;
DOI: 10.1007/s11139-012-9384-8
- Mit
S.Shimomura und I.Shiokawa:
"Algebraic
independence of certain numbers related to modular functions",
Functiones et Approximatio,
47.1
(2012), 121-141;
DOI: 10.7169/facm/2012.47.1.10
-
Mit D.Klyve und E.Tou:
"A
Zeta function for juggling sequences",
Journal of Combinatorics and Number Theory 4, no. 1 (2012),
53-65.
-
Mit M.Stein: "On
the value distribution of error sums for approximations with
rational numbers",
Integers, 12 (2012), A66, 1-28.
-
Mit A.Klauke: "Transcendence
results and continued fraction expansions obtained from a
combinatorial series",
Journal of Combinatorics and Number Theory 5, no. 1 (2013),
53-79.
-
Mit Yu.V. Nesterenko und I.Shiokawa: "Algebraic
independence of values of exponential type power series",
Moscow
Journal of Combinatorics and Number Theory 3, no. 3-4 (2013),
44-74 [280-310]
-
"On
error sums for square roots of positive integers with
applications to Lucas and Pell numbers",
Journal of Integer Sequences
17
(2014), Article 14.4.4,
https://cs.uwaterloo.ca/journals/JIS/VOL17/Elsner/elsner15.pdf
-
"On a generalization
of Hall’s theorem for sums of continued fractions",
Šiauliai Mathematical Seminar,
Šiauliai
University, Litauen, 9 (17) (2014),
43-59.
-
"Algebraic
independence results for values of Theta-constants",
Functiones et Approximatio, 52.1 (2015), 7-27;
DOI:
10.7169/facm/2015.52.1.1
-
"On
exponential-type sums formed by solutions of Pell’s equation",
Journal of Combinatorics and Number Theory 6, no. 3 (2015),
163-181.
-
"On
reciprocal sums formed by solutions of Pell's equation",
Integers 16 (2016), A88, 1-26.
- "On
error sum functions for approximations with arithmetic
conditions", From Arithmetic to Zeta-Functions, Number Theory in Memory of
Wolfgang Schwarz, (Jürgen Sander, Jörn Steuding, Rasa Steuding:
editors), 121-140, Springer 2016; ISBN 978-3-319-28202-2
- Mit Yohei Tachiya:
"Algebraic results for certain values of the Jacobi Theta-Constant
theta_3(tau)", Mathematica Scandinavica 123, no. 2 (2018), 249 -
272.
- Mit Jürgen Spilker:
"The Lucas property for linear recurrences of second order"
Elem. Math. 73 (2018), 151-160
- Mit Florian Luca und Yohei Tachiya: "Algebraic results for theta_3(mtau) and theta_3(ntau) of the
Jacobi-Theta Constant",
Moscow Journal of Combinatorics and Number Theory 8 - 1 (2019),
71 - 79.
- "Neues
von den Schwestern",
c't magazin für computer technik 3 (2019), 188 - 193.
- Mit Masanobu Kaneko
und Yohei Tachiya:
"Algebraic independence results for the values of the theta-constants and some
identities", J.Ramanujan Math. Soc. 35,
no. 1
(2020), 71- 80.
- Mit Niclas Technau:
"On linear relations for Dirichlet series formed by recursive
sequences of second order", Journal of the Australian Mathematical Society 110, no. 3
(2021), 406 - 430.
- Mit
Daniel Duverney, Masanobu Kaneko und Yohei Tachiya:
"A criterion of algebraic independence of values of modular
functions and an application to infinite products involving
Fibonacci and Lucas numbers",
Research in Number Theory,
https://doi.org/10.1007/s40993-022-00328-7
- Mit
Christopher Havens:
"Diophantine
Analysis around [1,2,3,...]",
in Number Theory in Memory of Eduard Wirsing, (Helmut
Maier, Jörn Steuding, Rasa Steuding: Editors), Springer, 2023,
119--143.
- Mit
Christopher Robin Havens:
"On Natural
Leaping Convergents of Regular Continued Fractions
and an Application to Linear Fractional Transformations",
Integers, vol. 23, (2023), A82, 1--35.
- Mit
Veekesh Kumar:
"On Algebraic Conditions for the Non-Vanishing of Linear Forms
in
Jacobi Theta-Constants"
Acta Mathematica Hungarica,
Online:
https://doi.org/10.1007/s10474-024-01449-4 (2024).