Homepage von
|
Prof.Dr.Carsten ELSNER Dr.rer.nat.habil.Dipl.Math. geb. am 10.11.1961 FHDW Hannover Freundallee 15 30173
Hannover ( E-Mail: mailto:carsten.elsner@fhdw.de |
|
Arbeitsgebiete: Analytische Zahlentheorie, Diophantische
Approximation, Universelle Differentialgleichungen
(Analytic Number Theory, Diophantine
Approximation, Universal Differential Equations)
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.(
"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
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-
Studia
Scientiarum Mathematicarum Hungarica 41
(1) (2004), 1-15.
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.
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,
"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,
"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.
Mit
S.Shimomura und I.Shiokawa: "Algebraic relations for
reciprocal sums of even terms in Fibonacci numbers"
(submitted paper)
Mit
S.Shimomura und I.Shiokawa: "Exceptional algebraic
relations for reciprocal sums of Fibonacci and Lucas numbers"
(submitted paper)
Mit
S.Shimomura und I.Shiokawa: "Algebraic independence
results for reciprocal sums of Fibonacci numbers"
(submitted paper)
Mit Marc Prévost: "Expansion
of Euler’s constant in terms of Zeta Numbers"
(submitted paper)
"On a generalization of
a formula of Ser and applications to the Riemann Zeta Function and to
(submitted paper)
"Series of error terms
for rational approximations of irrational numbers"
(submitted paper)
Nicht veröffentlichte Arbeiten
(Preprintreihe des Instituts für Mathematik der Universität
Hannover)
"Uniform
distribution of certain sequences of irrational numbers depending on primes in
arithmetic
progressions", (Nr. 289), 1999.
"On
sums with binomial coefficients", (Nr. 290), 1999.
"On
a generalization of Hall's theorem for sums of continued fractions", (Nr. 296), 1999.
"A
contribution to the metrical theory of diophantine approximation", (Nr. 300), 1999.
"On
a universal differential equation for analytic functions on the real
line", (Nr. 323), 2004.
Dissertation und Habilitationsschrift
Dissertation (thesis):
"Über Ausnahmemengen bei zwei
Varianten des Waringschen Problems für Kuben",
(On exceptional sets in
Waring's problem for cubes)
(Universität
Hannover, 1990)
Habilitationsschrift:
"Kongruenzbedingungen bei der
diophantischen Approximation von reellen Irrationalzahlen",
(Universität
Hannover, 1997)
E-Mail: Dr.Carsten Elsner
Letzte Änderung: 30.07.2010