# 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} }

- Published 2000 in computational complexity
DOI:10.1007/PL00001599

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. Inâ€¦Â CONTINUE READING

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#### References

##### Publications referenced by this paper.

Showing 1-10 of 18 references

## The Expressive Power of Voting Polynomials

View 14 Excerpts

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## Lower Bounds on Representing Boolean Functions as Polynomials in Zm

View 7 Excerpts

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## Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity

View 8 Excerpts

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## Complex polynomials and circuit lower bounds for modular counting

View 8 Excerpts

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## Representing Boolean functions as polynomials modulo composite numbers

View 10 Excerpts

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## A Note on the Power of Threshold Circuits

View 8 Excerpts

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## Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages in NCÂ¹

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## On the correlation of symmetric functions

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## Lower bounds for depth - three circuits with equals and mod - gates

## The Power of the Middle Bit of a #P Function

View 4 Excerpts