View More View Less
  • 1 University of Ostrava, 30. dubna 22, 701 03 Ostrava 1,, Czech Republic
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

  • [1]

    Choi, S. and Zhou, P., On linear independence of a certain multivariate infinite product, Canad. Math. Bull., 5, no. 1 (2008), 3246.

    • Search Google Scholar
    • Export Citation
  • [2]

    Deajim, A. and Siksek, S., On the ℚ-linear independence of the sums \sum\nolimits_{n = 1}^\infty {\tfrac{{\sigma _k (n)}} {{n!}}}, J. Number Theory, 131, no. 4 (2011), 745749.

    • Search Google Scholar
    • Export Citation
  • [3]

    Erdőos, P., Some Problems and Results on the Irrationality of the Sum of Infinite Series, J. Math. Sci., 10 (1975), 17.

  • [4]

    Erdőos, P., Erdőos problem no. 6, 1995 Prague Midsummer Combinatorial Work-shop, KAM Series (95-309), M. Klazar (ed.), (1995), page 5.

    • Export Citation
  • [5]

    Erdőos, P. and Straus, E. G., On the irrationality of certain series, Pacific Journal of Mathematics, Vol. 55, No. 1 (1974), 8592.

  • [6]

    Galochkin, A. I., On the linear independence of the values of functions satisfying Mahler’s functional equation. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1997), no. 5, 1417, 72; translation in Moscow Univ. Math. Bull., 52 (1997), no. 5, 1417.

    • Search Google Scholar
    • Export Citation
  • [7]

    Hančcl, J., Linearly unrelated sequences, Pacific Journal of Mathematics, Vol. 190, No. 2 (1999), 299310.

  • [8]

    Hančcl, J., A criterion for linear independence of series, Rocky Mountain J. Math., 34, no. 1 (2004), 173186.

  • [9]

    Hančcl J. and Kolouch O., Erdőos’ method for determining the irrationality of products, Bull. Aust. Math. Soc., 84, no. 3 (2011), 414424.

    • Search Google Scholar
    • Export Citation
  • [10]

    Hančcl, J. and Sobková, S., A general criterion for linearly unrelated sequences, Tsukuba Journal of Mathematics, Vol. 27, No. 2 (2003), 341357.

    • Search Google Scholar
    • Export Citation
  • [11]

    Hančcl, J. and Sobková, S., Special linearly unrelated sequences, J. Math. Kyoto Univ., vol. 46, no. 1, (2006), 3145.

  • [12]

    Hančcl, J. and Tijdeman, R., On the irrationality of factorial series, Acta Arith., 118, no. 4 (2005), 383401.

  • [13]

    Ivankov, P. L., On the linear independence of some numbers, (Russian) Mat. Zametki, 62 (1997), no. 3, 383390; translation in Math. Notes, 62 (1997), no. 3–4, 323328 (1998).

    • Search Google Scholar
    • Export Citation
  • [14]

    Keng, H. L., Introduction to number theory, Springer, (1982).

  • [15]

    Luca, F. and Tachiya, Y., Algebraic independence of infinite products generated by Fibonacci and Lucas numbers, Hokkaido Math. J., Vol. 43, No. 1 (2014), 120.

    • Search Google Scholar
    • Export Citation
  • [16]

    Nesterenko, Yu. V. and Shidlovskii, A. B., On the linear independence of values of E-functions, (Russian) Mat. Sb., 187 (1996), no. 8, 93108; translation in Sb. Math., 187 (1996), no. 8, 11971211.

    • Search Google Scholar
    • Export Citation
  • [17]

    Nishioka, K., Mahler functions and transcendence, Lecture Notes in Mathematics, 1631, Springer, (1996).

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu