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arXiv · 1804.04246

Bombieri-type theorem for convolution of arithmetic functions on Number field

Pranendu Darbar·Anirban Mukhopadhyay
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Abstract

Let $K$ be an imaginary quadratic number field of class number one and $\mathcal{O}_K$ be its ring of integers. We show that, if the arithmetic functions $f, g:\mathcal{O}_K\rightarrow \mathbb{C}$ both have level of distribution $\vartheta$ for some $0<\vartheta\leq 1/2$ then the Dirichlet convolution $f*g$ also have level of distribution $\vartheta$.

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Pranendu Darbar, Anirban Mukhopadhyay. 2018-04-11. Bombieri-type theorem for convolution of arithmetic functions on Number field. https://arxiv.org/abs/1804.04246

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