Biases in prime factorizations and Liouville functions for arithmetic progressions
Biases in prime factorizations and Liouville functions for arithmetic progressions
We introduce a refinement of the classical Liouville function to primes in arithmetic progressions. Using this, we show that the occurrence of primes in the prime factorizations of integers depends on the arithmetic progressions to which the given primes belong. Supported by numerical tests, we are led to consider analogues …