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Let $T_aD_b(n)$ and $T_aD'_b(n)$ denote respectively the number of representations of a positive integer $n$ by $a(x^2-x)/2 +b(4y^2-3y)$ and $a(x^2-x)/2 +b(4y^2-y)$. Similarly, let $S_aD_b(n)$ and $S_aD'_b(n)$ denote respectively the number of representations of $n$ by $ax^2 +b(4y^2-3y)$ and $ax^2 +b(4y^2-y)$. In this paper, we prove 162 formulas for these functions.
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참고문헌 (20)
참고문헌 신청
N. D. Baruah / 2012 / The number of representations of a number as sums of various polygonal numbers / Integers 12:16
B. C. Berndt / 1991 / Ramanujan's Notebooks. Part III / Springer-Verlag
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathematical Society
Heng Huat Chan / 2015 / Theta series associated with certain positive definite binary quadratic forms / Acta Arithmetica 169(4):331~356
Michael D. Hirschhorn / 2005 / The number of representations of a number by various forms / Discrete Mathematics 298(1-3):205~211
B. C. Berndt / 1991 / Ramanujan's Notebooks. Part III / Springer-Verlag
B. C. Berndt / 2006 / Number Theory in the Spirit of Ramanujan / American Mathematical Society
Heng Huat Chan / 2015 / Theta series associated with certain positive definite binary quadratic forms / Acta Arithmetica 169(4):331~356
Michael D. Hirschhorn / 2005 / The number of representations of a number by various forms / Discrete Mathematics 298(1-3):205~211
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