Sum-product theorem and exponential sum estimates in residue classes with modulus involving few prime factors

In this Note, we extend the results of Bourgain, Konyagin and Glibichuk to certain composite moduli q involving few ‘large’ primes. First a ‘sum-product’ theorem for subsets A of Zq is obtained, ensuring that |A+A|+|A.A|>c|A|1+ɛ provided |A