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In this paper we deduce the number of representations of a positive integer n by each of the six triangular forms as $${\frac{1}{2}}x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+{\frac{1}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+{\frac{3}{2}}x_4(x_4+1),\\x_1(x_1+1)+{\frac{3}{2}}x_2(x_2+1)+{\frac{3}{2}}x_3(x_3+1)+3x_4(x_4+1),\\{\frac{1}{2}}x_1(x_1+1)+{\frac{1}{2}}x_2(x_2+1)+3x_3(x_3+1)+3x_4(x_4+1).$$
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참고문헌 (5)
참고문헌 신청
A. Alaca / 2007 / Nineteen quaternary quadratic forms / Acta Arith. 130(3):277~310
A. Alaca / 2008 / Theta function identities and representations by certain quaternary quadratic forms / International Journal of Number Theory 4(2):219~239
A. Alaca / 2008 / Theta function identi-ties and representations by certain quaternary quadratic forms II / International Mathematical Forum 3(12):539~579
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathemat-ical Society
K. S. Williams / 2011 / Number Theory in the Spirit of Liouville / London Mathematical Society
A. Alaca / 2008 / Theta function identities and representations by certain quaternary quadratic forms / International Journal of Number Theory 4(2):219~239
A. Alaca / 2008 / Theta function identi-ties and representations by certain quaternary quadratic forms II / International Mathematical Forum 3(12):539~579
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathemat-ical Society
K. S. Williams / 2011 / Number Theory in the Spirit of Liouville / London Mathematical Society
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