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arXiv · 1212.4348

On partial sums of the M\"obius and Liouville functions for number fields

Yusuke Fujisawa·Makoto Minamide
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Abstract

Landau examined the partial sums of the M\"obius function and the Liouville function for a number field $K$. First we shall try again the same problem by using a new Perron's formula due to Liu and Ye. Next we consider the equivalent theorem of the grand Riemann hypothesis for the Dedekind zeta-function of $K$ and that of the prime ideal theorem.

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Yusuke Fujisawa, Makoto Minamide. 2012-12-18. On partial sums of the M\"obius and Liouville functions for number fields. https://arxiv.org/abs/1212.4348

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