Multiplicative functions f with |sum_{n≤x} f(n)| bounded by x (log Q)^{A-D-1}/(log x)^A and |Λ_f|≤DΛ admit parameters m and Q_j such that Re(f(p)+j) averages to O(1) over primes in intervals [Q_{j+1}, Q_j) for j≥m.
Sachpazis,On multiplicative functions with small partial sums.Int
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A logarithmic structure theorem for multiplicative functions with small partial sums
Multiplicative functions f with |sum_{n≤x} f(n)| bounded by x (log Q)^{A-D-1}/(log x)^A and |Λ_f|≤DΛ admit parameters m and Q_j such that Re(f(p)+j) averages to O(1) over primes in intervals [Q_{j+1}, Q_j) for j≥m.