Signed sequences and completely multiplicative functions are constructed with small signed harmonic sums and logarithmic means decaying like exp(-c N^{1/3}/(log N)^{1/3}) infinitely often.
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Small values of signed harmonic sums and logarithmic means of multiplicative functions
Signed sequences and completely multiplicative functions are constructed with small signed harmonic sums and logarithmic means decaying like exp(-c N^{1/3}/(log N)^{1/3}) infinitely often.