[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.
[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.
Year 2014,
Volume: 63 Issue: 2, 135 - 145, 01.08.2014
[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.
[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.
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. August 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, no. 2 (August 2014): 135-45. https://doi.org/10.1501/Commua1_0000000719.
EndNote
Köklüce B (August 1, 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., vol. 63, no. 2, pp. 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 (August 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, vol. 63, no. 2, 2014, pp. 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.