A question of Erdös, known as the Erdös discrepancy problem, asks if any arithmetic sequence of +-1 has infinite discrepancy. This has became a Theorem by T. Tao in 2015. A key step in its proof was to show that a completely multiplicative function assuming only +-1 values has unbounded partial sums. In this talk I will consider similar questions for multiplicative functions supported on the squarefree and cubefree integers.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246