Ir al contenido

Documat


New approach for Somos’s Dedekind eta-function identities of level 6

  • Anu Radha, D. [1] ; Srivatsa Kumar, B. R. [1] ; Shruthi [1]
    1. [1] Manipal Academy of Higher Education.
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 1, 2021, págs. 187-198
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-2021-01-0012
  • Enlaces
  • Resumen
    • In the present work, we prove few new Dedekind eta-function identities of level 6 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 6 proved by B. R. Srivatsa Kumar et al. As an application of this, we establish colored partition identities.

  • Referencias bibliográficas
    • C. Adiga, M. S. M. Naika, and K. Shivashankara, “On some P-Q eta-function identities of Ramanujan”, Indian journal of mathematics, vol. 44,...
    • C. Adiga, T. Kim, M. S. M. Naika, and H. S. Madhusudhan, “On Ramanujan’s cubic continued fraction and explicit evaluations of theta-functions”,...
    • C. Adiga, N. A. S Bulkhali, D. Ranganatha, and H. M. Srivastava, “Some new modular relations for the Rogers-Ramanujan type functions of order...
    • N. D. Baruah, “Modular equations for Ramanujan’s cubic continued fraction”, Journal mathematics analysis applications, vol. 268, no. 1, pp....
    • N. D. Baruah, “On some of Ramanujan’s Schläfli-type ‘mixed’ modular equations”, Journal number theory, vol. 100, no. 2, pp. 270-294, Jun....
    • B. C. Berndt, Ramanujan's notebooks, vol. 3. New York, NY: Springer, 1991, doi: 10.1007/978-1-4612-0965-2
    • B. C. Berndt, Ramanujan's notebooks, vol. 4. New York, NY: Springer, 1996, doi: 10.1007/978-1-4612-0879-2
    • Z. Cao, “On Somos’s dissection identities”, Journal of mathematical analysis and applications, vol. 365, no. 2, pp. 659-667, May 2010, doi:...
    • S. -S. Huang, “On modular relation for the Göllnitz-Gordon functions with applications to partitions”, Journal number theory, vol 68, no....
    • M. S. M. Naika, “A note on cubic modular equations of degree two *”, Tamsui Oxford Journal Mathematics Society, vol. 22, no. 1, pp. 1-8, 2006....
    • S. Ramanujan, Notebooks, 2 vols. Bombay: Tata Institute of Fundamental Research, 1957.
    • S. Ramanujan, The lost notebook and other unpublished papers, New Delhi: Narosa, 1988.
    • N. Saikia, “Modular identities and explicit values of a continued fraction of order twelve”, JP journal of algebra, number theory and applications,...
    • M. Somos, Personal communication [e-mail], October 24, 2004.
    • B. R. Srivatsa Kumar and R. G. Veeresha, “Partition identities arising from Somos’s theta function identities”, Annali Dell ‘Universita’ Di...
    • B. R. Srivatsa Kumar and D. Anu Radha, “Somos’s theta-function identities of level 10”, Turkish journal of mathematics, vol. 42, pp. 763-773,...
    • B. R. Srivatsa Kumar, K. R. Rajanna, and R. Narendra, “New theta-function identities of level 6 in the spirit of Ramanujan”, Mathematical...
    • B. R. Srivatsa Kumar, K. R. Rajanna, and R. Narendra, “Theta-function identities of level 8 and its application to partitions”, Afrika matematika,...
    • K. R. Vasuki, T. G. Sreeramamurthy, “A note on P-Q modular equations”, Tamsui Oxford Journal Mathematics Sciences, vol. 21, no. 2, pp. 109-120,...
    • K. R. Vasuki, “On some of Ramanujan’s P-Q modular equations”, Journal Indian Mathematical Society, vol. 73, no. 3-4, pp. 131-143, 2006.
    • K. R. Vasuki and R. G. Veeresha, “On Somos’s theta-function identities of level 14”, Ramanujan journal, vol. 42, pp. 131-144, Jan. 2017, doi:...
    • J. Yi, “Theta-function identities and the explicit formulas for theta function and their applications”, Journal mathematics analysis applications,...
    • B. Yuttanan, “New modular equations in the spirit of Ramanujan”, Ramanujan journal, vol. 29, pp. 257-272, Dec. 2012, doi: 10.1007/s11139-012-9399-1

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno