Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
| Autor: | Park, Poo-Sung |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | If a multiplicative function $f$ is commutable with a quadratic form $x^2+xy+y^2$, i.e., \[ f(x^2+xy+y^2) = f(x)^2 + f(x)\,f(y) + f(y)^2, \] then $f$ is the identity function. In other hand, if $f$ is commutable with a quadratic form $x^2-xy+y^2$, then $f$ is one of three kinds of functions: the identity function, the constant function, and an indicator function for $\mathbb{N}\setminus p\mathbb{N}$ with a prime $p$. Comment: Under review |
| Databáze: | arXiv |
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