Analytic versions of the zero divisor conjecture

One of the most famous and frustrating problems in algebra is the zero divisor conjecture. In this work we study some analytical versions of this conjecture. We will give sufficient conditions to determine when elements of CG are uniform non zero divisors, we also give sufficient conditions to determine when elements of CG are p-zero divisors. Examples of p-zero divisors will also be given. Also a measure theoretic approach to the zero divisor conjecture will be given.