ON SOME QUESTIONS OF PARTITIO NUMERORUM: TRES CUBI
This paper is concerned with the function r3(n), the number of representations of n as the sum of at most three positive cubes, $$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$ , Our understanding of this function is surprisingly poor, and we examine various ave...
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| Veröffentlicht in: | Glasgow mathematical journal 2021-01, Vol.63 (1), p.223-244 |
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| creator | VAUGHAN, R. C. |
| description | This paper is concerned with the function r3(n), the number of representations of n as the sum of at most three positive cubes,
$$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$
, Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular
$${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$
and
$${\sum_{\substack{ n\le x\\ n\equiv a\,\mathrm{mod}\,q }} r_3(n).\}$$ |
| doi_str_mv | 10.1017/S0017089520000142 |
| format | Article |
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$$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$
, Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular
$${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$
and
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$$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$
, Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular
$${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$
and
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$$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$
, Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular
$${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$
and
$${\sum_{\substack{ n\le x\\ n\equiv a\,\mathrm{mod}\,q }} r_3(n).\}$$</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0017089520000142</doi><tpages>22</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0017-0895 |
| ispartof | Glasgow mathematical journal, 2021-01, Vol.63 (1), p.223-244 |
| issn | 0017-0895 1469-509X |
| language | eng |
| recordid | cdi_proquest_journals_2469961224 |
| source | Cambridge University Press Journals Complete |
| subjects | Cubes |
| title | ON SOME QUESTIONS OF PARTITIO NUMERORUM: TRES CUBI |
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