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Braun,s Conjecture

المؤلف:  Flath, A. and Zulauf, A.

المصدر:  "Does the Möbius Function Determine Multiplicative Arithmetic?" Amer. Math. Monthly 102

الجزء والصفحة:  ...

16-8-2020

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Braun's Conjecture

Let {b_1,b_2,...}" src="https://mathworld.wolfram.com/images/equations/BraunsConjecture/Inline1.gif" style="height:15px; width:92px" /> be an infinite Abelian semigroup with linear order  such that  is the unit element and  implies  for . Define a Möbius function  on  by  and

for , 3, .... Further suppose that  (the true Möbius function) for all . Then Braun's conjecture states that

for all .

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REFERENCES:

Flath, A. and Zulauf, A. "Does the Möbius Function Determine Multiplicative Arithmetic?" Amer. Math. Monthly 102, 354-256, 1995.