Carsten Elsner

 

Publizierte Schriften

  1. "On Mahler's approximation function for powers of certain algebraic numbers",
         Studia Scientiarum Mathematicarum Hungarica 27 (1992), 147-158.
  2. "On the approximation of continuous functions by C(infinity) -solutions of third order algebraic differential equations",
    Mathematische Nachrichten 157 (1992), 235-241.
  3. "On a sequence transformation with integral coefficients for Euler's constant",
         Proceedings of the AMS 123, no.5 (1995), 1537-1541.
  4. "On the approximation of irrational numbers with rationals restricted by congruence relations",
         The Fibonacci Quarterly 34, no.1 (1996), 18-29.
  5. "On inhomogeneous approximation to irrational numbers with arithmetical conditions",
         Abh.Math.Sem.Univ.Hamburg 66 (1996), 223-228.
  6. "On the approximation of irrationals by rationals",
         Mathematische Nachrichten 189 (1998), 243-256.
  7. "A metric result concerning the approximation of real numbers by continued fractions",
         The Fibonacci Quarterly 36, no.4 (1998), 290-294.
  8. Mit J.W.Sander: "On the exact height of integer-detecting sequences",
     Journal of Number Theory 73 (1998), 1-13.
  9. "A universal functional equation",
         Proceedings of the AMS 127, no. 1 (1999), 139-143.
  10. "On arithmetic properties of the convergents of Euler's number",
         Colloquium Mathematicum 79, no. 1 (1999), 133-145.
  11. "On rational approximations with denominators from thin sets",
     Abh.Math.Sem.Univ.Hamburg 69 (1999), 229-235. 
  12. "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. 
  13. "Der Dialog der Schwestern",
    c't magazin für computer technik 25 (1999), 288-296. 
  14. "On diophantine approximations with rationals restricted by arithmetical conditions",
         The Fibonacci Quarterly 38, no.1 (2000), 25-34. 
  15. "A universal differential equation of degree six",
         Journal of Mathematical Analysis and Applications 244 (2000), 533-541. 
  16. 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. 
  17. "Über eine effektive Konstruktion großer Mengen algebraisch unabhängiger Zahlen",
     Mathematische Semesterberichte 47 (2000), 243-256. 
  18. "On arithmetic properties of the solutions of a universal differential equation at algebraic points",
         Journal of Mathematical Analysis and Applications 256 (2001), 324-338. 
  19. Mit J.W.Sander und J.Steuding: "Kettenbrüche als Summe ebensolcher" (English version),
         Mathematica Slovaca 51 (2001), no.3, 281-293. 
  20. "Das chinesische Labyrinth",
    c't magazin für computer technik 21 (2001), 308-312; (www.heise.de/ct Rubrik Magazin). 
  21. "Diophantine approximations with arithmetic restrictions and an application to trigonometric functions",
         Analysis 21 (2001), 327-337. 
  22. "On simultaneous approximations of continuous functions by solutions of an algebraic differential equation",
         Acta Sci.Math.(Szeged) 67 (2001), 697-708. 
  23. "On an universal functional equation of degree six"
         Applied Nonlinear Analysis 9 (2002) no.3, 23-29. 
  24. "On rational approximation with denominators from thin sets, I I ",
         Abh.Math.Sem.Univ.Hamburg 72 (2002), 35-45. 
  25. "On inhomogeneous diophantine approximations with rational terms and applications to elliptic and trigonometric functions",
     Resultate der Mathematik 42 (2002), 235-251. 
  26. "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.
  27. "On rational approximations by Pythagorean numbers",
         The Fibonacci Quarterly 41 no.2 (2003), 98-104. 
  28. "On the approximation of continuous functions by analytic solutions of universal functional-differential equations",
         Studia Scientiarum Mathematicarum Hungarica 41 (1) (2004), 1-15. 
  29. "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. 
  30. "Höhere Mathematik an der Balkenwaage"
         Elemente der Mathematik 59 (2004), 151-170.  
  31. "On a method to transform algebraic differential equations into universal equations",
         Abh.Math.Sem.Univ.Hamburg  74 (2004), 33-48. 
  32. "On recurrence formulae for sums involving binomial coefficients",
         The Fibonacci Quarterly 43 no.1 (2005), 31-45. 
  33. "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. 
  34. "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.
  35. "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. 
  36. 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. 
  37. 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. 
  38. 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. 
  39. "On a sequence transformation with integral coefficients for Euler’s constant, II",
    Journal of Number Theory 124 (2007), 442 – 453.     
  40. Mit S.Shimomura und I.Shiokawa:  "Algebraic relations for reciprocal sums of Fibonacci numbers",
         Acta Arithmetica 130.1 (2007), 37 – 60.     
  41. 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.     
  42. Mit T.Komatsu:  "A recurrence formula for leaping convergents of non-regular continued fractions",
    Linear Algebra and its Applications 428 (2008), 824 – 833. 
  43. 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. 
  44. "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
  45. Mit S.Shimomura und I.Shiokawa:  "Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers",
         Ramanujan Journal, 17 (2008), 429 – 446. 
  46. 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).     
  47. "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. 
  48. 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. 
  49. Mit T.Komatsu und I.Shiokawa:  "On convergents formed from Diophantine equations",
    Glasnik Matematicki, 44 no.2 (2009), 267 – 284.
  50. Mit S.Shimomura und I.Shiokawa:  "A remark on Nesterenko’s theorem for Ramanujan functions",
    Ramanujan Journal, 21, no. 2 (2010), 211 – 221. 
  51. "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.
  52. 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. 
  53. "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. 
  54. "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 
  55. Mit S.Shimomura und I.Shiokawa:  "Algebraic independence results for reciprocal sums of Fibonacci numbers",
         Acta Arithmetica 148.3 (2011), 205 – 223. 
  56. 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. 
  57. 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 
  58. 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 
  59. 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. 
  60. 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. 
  61. 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 
  62. Mit I.Shiokawa: "On algebraic relations for Ramanujan’s functions",
    Ramanujan Journal, 29 (2012), 273-294;
    DOI: 10.1007/s11139-012-9384-8 
  63. 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 
  64. Mit D.Klyve und E.Tou:  "A Zeta function for juggling sequences",
    Journal of Combinatorics and Number Theory 4, no. 1 (2012), 53-65. 
  65. Mit M.Stein: "On the value distribution of error sums for approximations with rational numbers",
    Integers, 12 (2012), A66, 1-28. 
  66. 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. 
  67. 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]
  68. "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 
  69. "On a generalization of Hall’s theorem for sums of continued fractions",
    Šiauliai Mathematical Seminar, Šiauliai University, Litauen, 9 (17) (2014), 43-59. 
  70. "Algebraic independence results for values of Theta-constants",
         Functiones et Approximatio, 52.1 (2015), 7-27;
     DOI:  10.7169/facm/2015.52.1.1 
  71. "On exponential-type sums formed by solutions of Pell’s equation",
     Journal of Combinatorics and Number Theory 6, no. 3 (2015), 163-181.
  72. "On reciprocal sums formed by solutions of Pell's equation", Integers 16 (2016), A88, 1-26.
  73. "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
  74. Mit Yohei Tachiya:                                                              "Algebraic results for certain values of the Jacobi Theta-Constant theta_3(tau)",                                                                 Mathematica Scandinavica 123, no. 2 (2018), 249 - 272.
  75. Mit Jürgen Spilker:                                                                         "The Lucas property for linear recurrences of second order"              Elem. Math. 73 (2018), 151-160
  76. 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.    
  77. "Neues von den Schwestern",                                                             c't magazin für computer technik 3 (2019), 188 - 193.
  78.  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. 
  79. 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.
  80. 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
  81. 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.
  82. 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.

Seit 1992.