Braun's Conjecture

Let $B={b_1,b_2,...}$ 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 .

See also

Möbius Problem

Explore with Wolfram|Alpha

More things to try:

References

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

Referenced on Wolfram|Alpha

Braun's Conjecture

Cite this as:

Weisstein, Eric W. "Braun's Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BraunsConjecture.html

Subject classifications