On hybrid moments of $$\Delta _2(x)$$ and $$\Delta _3(x)$$
| Autor: | Yoshio Tanigawa, Wenguang Zhai, Xiaodong Cao |
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| Rok vydání: | 2021 |
| Předmět: |
Delta
Algebra and Number Theory Mathematics::Number Theory 010102 general mathematics Natural number 0102 computer and information sciences Function (mathematics) 01 natural sciences Combinatorics Number theory 010201 computation theory & mathematics Product (mathematics) Asymptotic formula 0101 mathematics Mathematics |
| Zdroj: | The Ramanujan Journal. 58:597-631 |
| ISSN: | 1572-9303 1382-4090 |
| DOI: | 10.1007/s11139-021-00431-w |
| Popis: | Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to denote the error term in the asymptotic formula of the summatory function of $$d_k(n).$$ The aim of this paper is to study the hybrid moments of $$\Delta _2(x)$$ and $$\Delta _3(x)$$ . The higher power moments of $$\Delta _2(x)$$ are also studied. |
| Databáze: | OpenAIRE |
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