Euler function E(x) is defined as: E(x) = \prod_{i=1}^{\infty} (1 - x^i). It is a well-known modular form in mathematics, and is the inverse of the generating function for partition function. We investigate the arithmetic complexity of computing this function. Let E_n(x) = \prod_{i=1}^n (1 - x^i), so that E(x) = \lim_{x\mapsto \infty} E_n(x). The family of polynomials \{ E_n(x) \} can clearly be computed by an arithmetic circuits of size O(n^2) over Z with unbounded fanin addition and multiplication gates. We show that if every arithmetic circuit family computing \{ E_n(x) \} over Z is of size n^{\Omega(1)}, then computing the permanent polynomial requires exponential sized arithmetic circuits over Z.