A modified M\"obius $\mu$-function
  We investigate a modified M\"obius $\mu$-function which is related to an infinite product of shifted Riemann zeta-functions. We prove conditional and unconditional upper and lower bounds for its summatory function, and, finally, we discuss relations with Riemann's hypothesis. 
Rasa Steuding, J\"orn Steuding, L\'aszl\'o T\'oth
math.NT