Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity

Sen-Shan Huang

Acta Arithmetica (1997)

  • Volume: 80, Issue: 1, page 49-60
  • ISSN: 0065-1036

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Sen-Shan Huang. "Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity." Acta Arithmetica 80.1 (1997): 49-60. <http://eudml.org/doc/207026>.

@article{Sen1997,
author = {Sen-Shan Huang},
journal = {Acta Arithmetica},
keywords = {continued fraction; convergent; primitive root of unity; partition modulo s; Rogers-Ramanujan continued fraction; primitive roots of unity},
language = {eng},
number = {1},
pages = {49-60},
title = {Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity},
url = {http://eudml.org/doc/207026},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Sen-Shan Huang
TI - Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 1
SP - 49
EP - 60
LA - eng
KW - continued fraction; convergent; primitive root of unity; partition modulo s; Rogers-Ramanujan continued fraction; primitive roots of unity
UR - http://eudml.org/doc/207026
ER -

References

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  1. [1] P. Bachmann, Niedere Zahlentheorie, New York, 1991. 
  2. [2] B. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991. Zbl0733.11001
  3. [3] L. Lorentzen and H. Waadeland, Continued Fractions with Applications, North-Holland, Amsterdam, 1992. Zbl0782.40001
  4. [4] A. I. Markushevich, Theory of Functions of a Complex Variable, English translation by R. A. Silverman, Chelsea, New York, 1985. 
  5. [5] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. Zbl0639.01023
  6. [6] S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957. 
  7. [7] I. Schur, Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche, S.-B. Preuss. Akad. Wiss. Phys.-Math. Kl. (1917), 302-321. Zbl46.1448.02
  8. [8] H. Stern, Ueber eine der Theilung der Zahlen ähnliche Untersuchung und deren Anwendung auf die Theorie der quadratischen Reste, J. Reine Angew. Math. 61 (1863), 66-94. 
  9. [9] H. Stern, Zur Theorie der quadratischen Reste, ibid., 334-349. 
  10. [10] R. Daublebsky v. Sterneck, Ein Analogon zur additiven Zahlentheorie, Sitzungsber. Wiener Akad. 111 (1902), 1567-1601. 
  11. [11] R. Daublebsky v. Sterneck, Ein Analogon zur additiven Zahlentheorie, ibid. 113 (1904), 326-340. Zbl34.0214.02
  12. [12] R. Daublebsky v. Sterneck, Über die Kombinationen der Potenzreste einer Primzahl zu bestimmten Summen, ibid. 114 (1905), 711-758. 

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