Overpartitions and ternary quadratic forms
| Autor: | Xinhua Xiong |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Mathematics::Complex Variables Mathematics::Number Theory High Energy Physics::Phenomenology 010102 general mathematics 0102 computer and information sciences Congruence relation 01 natural sciences Combinatorics Number theory 010201 computation theory & mathematics 0101 mathematics Ternary operation Mathematics |
| Zdroj: | The Ramanujan Journal. 42:429-442 |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-016-9773-5 |
| Popis: | Let \(\overline{p}(n)\) denote the number of overpartitions of n. Recently, Mahlburg showed that \(\overline{p}(n) \equiv 0 \pmod {64}\) and Kim showed that \(\overline{p}(n) \equiv 0 \pmod {128}\) for almost all integers n. In this paper, with the help of some ternary quadratic forms, we prove that \(\overline{p}(n) \equiv 0 \pmod {256}\) for almost all integers n, which was conjectured by Mahlburg. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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