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The number of representations of a positive integer by triangular, square and decagonal numbers

Uha Isnaini|Ray Melham|Pee Choon Toh
대한수학회 (The Korean Mathematical Society)|2019.09|대한수학회보 (Bulletin of the KMS)|제56권 제5호|pp. 1143-1157|DOI 10.4134/BKMS.b180914

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키워드

representations by binary quadratic forms
주제분류수학

초록

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.

Abstract

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.

참고문헌 (20)

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