The Bombieri 
-norm
of a polynomial
 |
(1)
|
is defined by
![[Q]_p=[sum_(i=0)^n(n; i)^(1-p)|a_i|^p]^(1/p),](/images/equations/BombieriNorm/NumberedEquation2.svg) |
(2)
|
where 
is a binomial coefficient. The most remarkable
feature of Bombieri's norm is that given polynomials 
and 
such that 
, then Bombieri's inequality
![[R]_2[S]_2<=(n; m)^(1/2)[Q]_2](/images/equations/BombieriNorm/NumberedEquation3.svg) |
(3)
|
holds, where 
is the degree of 
,
and 
is the degree of either 
or 
. This theorem captures the heuristic that if 
and 
have big coefficients, then so does 
, i.e., there can't be too much cancellation.
