BibTex RIS Kaynak Göster

REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS

Yıl 2014, Cilt: 63 Sayı: 2, 135 - 145, 01.08.2014
https://doi.org/10.1501/Commua1_0000000719

Kaynakça

  • [4] ¸S. Alaca, K.S. Williams, The number of representation of a positive integer by certain octonary quadratic forms, Funct. Approx. 43 (1) (2010), 45-54.
  • [5] A. Alaca, ¸S. Alaca, K.S. Williams, Fourteen octonary quadratic forms, Int. J. Number Theory 6 (2010), 37-50.
  • [6] A. Alaca, ¸S. Alaca, K.S. Williams, Seven octonary quadratic forms, Acta Arith. 135 (2008), 339-350.
  • [7] A. Alaca, ¸S. Alaca, M. F. Lemire, K.S. Williams, Nineteen quaternary quadratic forms, Acta Arith. 130 (2007), 277-310.
  • [8] J.W.L. Glaisher, On the square of the series in which the coe¢ cients are the sums of the divisors of the exponents, Mess. Math. 14 (1885), 156-163.
  • [9] J.G. Huard, Z.M. Ou, B.K. Spearman, K.S. Williams, Elementary Theory for the Millenium II, edited by M.A. Bennet, B. C. Berndt, N. Boston, H. G. Diamond, A. J. H. Hildebrand, and W. Philipp, A. K. Peters, Natick, Massachusetts, 2002, pp. 229-274.
  • [10] C.G.J. Jacobi, Fundamenta nova theoriae functionum ellipticarum, 1829, in Gesammelte Werke, Erster Band (Chelsea Publishing Co., New York, 1969), pp. 49ñ239.
  • [11] B. Kˆkl¸ce, The representation numbers of three octonary quadratic forms, Int. J. Number Theory 9 (2013), 505-516.
  • [12] B. Kˆkl¸ce, On the number of representation of positive integers by some octonary quadratic forms, 2nd International Eurasian Conference on Mathematical Sciences and Applications ( IECMSA), Sara jevo, Bosnia and Herzegovina, August, 2013.
  • [13] G. MelÖ, On some modular identities, Number Theory (K. Gyˆry, A.Pethˆ, and V. Sos, eds), de Gruyter, Berlin, 1998, pp. 371-382.
  • [14] G. MelÖ, Some Problems in Elementary Number Theory and Modular Forms, Ph. D. thesis, University of Pisa, 1998.
  • [15] K.S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184.
  • [16] K.S. Williams, A cubic transformation formula for 2F( 1 2 ; 2 3 ; 1; z) and some arithmetic convolution formulae, Math. Proc. Cambridge Philos. Soc. 137 (2004), 519-539.
  • [17] K.S. Williams, An arithmetic proof of Jacobiís eight squares theorem, Far East J. Math. Sci. 3 (2001), 1001-1005. , PaciÖc J. Math. 228 (2006), 387-396.
Yıl 2014, Cilt: 63 Sayı: 2, 135 - 145, 01.08.2014
https://doi.org/10.1501/Commua1_0000000719

Kaynakça

  • [4] ¸S. Alaca, K.S. Williams, The number of representation of a positive integer by certain octonary quadratic forms, Funct. Approx. 43 (1) (2010), 45-54.
  • [5] A. Alaca, ¸S. Alaca, K.S. Williams, Fourteen octonary quadratic forms, Int. J. Number Theory 6 (2010), 37-50.
  • [6] A. Alaca, ¸S. Alaca, K.S. Williams, Seven octonary quadratic forms, Acta Arith. 135 (2008), 339-350.
  • [7] A. Alaca, ¸S. Alaca, M. F. Lemire, K.S. Williams, Nineteen quaternary quadratic forms, Acta Arith. 130 (2007), 277-310.
  • [8] J.W.L. Glaisher, On the square of the series in which the coe¢ cients are the sums of the divisors of the exponents, Mess. Math. 14 (1885), 156-163.
  • [9] J.G. Huard, Z.M. Ou, B.K. Spearman, K.S. Williams, Elementary Theory for the Millenium II, edited by M.A. Bennet, B. C. Berndt, N. Boston, H. G. Diamond, A. J. H. Hildebrand, and W. Philipp, A. K. Peters, Natick, Massachusetts, 2002, pp. 229-274.
  • [10] C.G.J. Jacobi, Fundamenta nova theoriae functionum ellipticarum, 1829, in Gesammelte Werke, Erster Band (Chelsea Publishing Co., New York, 1969), pp. 49ñ239.
  • [11] B. Kˆkl¸ce, The representation numbers of three octonary quadratic forms, Int. J. Number Theory 9 (2013), 505-516.
  • [12] B. Kˆkl¸ce, On the number of representation of positive integers by some octonary quadratic forms, 2nd International Eurasian Conference on Mathematical Sciences and Applications ( IECMSA), Sara jevo, Bosnia and Herzegovina, August, 2013.
  • [13] G. MelÖ, On some modular identities, Number Theory (K. Gyˆry, A.Pethˆ, and V. Sos, eds), de Gruyter, Berlin, 1998, pp. 371-382.
  • [14] G. MelÖ, Some Problems in Elementary Number Theory and Modular Forms, Ph. D. thesis, University of Pisa, 1998.
  • [15] K.S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184.
  • [16] K.S. Williams, A cubic transformation formula for 2F( 1 2 ; 2 3 ; 1; z) and some arithmetic convolution formulae, Math. Proc. Cambridge Philos. Soc. 137 (2004), 519-539.
  • [17] K.S. Williams, An arithmetic proof of Jacobiís eight squares theorem, Far East J. Math. Sci. 3 (2001), 1001-1005. , PaciÖc J. Math. 228 (2006), 387-396.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Bülent Köklüce Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 63 Sayı: 2

Kaynak Göster

APA Köklüce, B. (2014). REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(2), 135-145. https://doi.org/10.1501/Commua1_0000000719
AMA Köklüce B. REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2014;63(2):135-145. doi:10.1501/Commua1_0000000719
Chicago Köklüce, Bülent. “REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, sy. 2 (Ağustos 2014): 135-45. https://doi.org/10.1501/Commua1_0000000719.
EndNote Köklüce B (01 Ağustos 2014) REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 2 135–145.
IEEE B. Köklüce, “REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 63, sy. 2, ss. 135–145, 2014, doi: 10.1501/Commua1_0000000719.
ISNAD Köklüce, Bülent. “REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/2 (Ağustos 2014), 135-145. https://doi.org/10.1501/Commua1_0000000719.
JAMA Köklüce B. REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:135–145.
MLA Köklüce, Bülent. “REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 63, sy. 2, 2014, ss. 135-4, doi:10.1501/Commua1_0000000719.
Vancouver Köklüce B. REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(2):135-4.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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