A complex-number Fourier technique for lower bounds on the Mod-m degree

@article{Green2000ACF,
  title={A complex-number Fourier technique for lower bounds on the Mod-m degree},
  author={Frederic Green},
  journal={computational complexity},
  year={2000},
  volume={9},
  pages={16-38}
}
We say an integer polynomial p, on Boolean inputs, weakly m-represents a Boolean function f if p is nonconstant and is zero (mod m), whenever f is zero. In this paper we prove that if a polynomial weakly m-represents the Mod q function on n inputs, where q and m are relatively prime and m is otherwise arbitrary, then the degree of the polynomial is $ \Omega(n) $ . This generalizes previous results of Barrington, Beigel and Rudich, and Tsai, which held only for constant or slowly growing m. In… CONTINUE READING

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