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

Makoto Minamide; Yusuke Fujisawa

arxiv: 1212.4348 · v1 · pith:HUBQMEAEnew · submitted 2012-12-18 · 🧮 math.NT

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

Yusuke Fujisawa , Makoto Minamide This is my paper

classification 🧮 math.NT

keywords functionliouvillenumberobiuspartialsumstheoremconsider

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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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M\"obius formulas for densities of sets of prime ideals
math.NT 2019-07 unverdicted novelty 7.0

If a set S of prime ideals has natural density δ(S), then δ(S) equals the negative limit as X goes to infinity of the sum of μ(a)/N(a) over ideals a in D(K,S) with norm at most X.