Weyl's Inequality in Number Theory
In number theory, Weyl's inequality, named for Hermann Weyl, states that if M, N, a and q are integers, with a and q coprime, q > 0, and f is a real polynomial of degree k whose leading coefficient c satisfies
for some t greater than or equal to 1, then for any positive real number one has
This inequality will only be useful when
for otherwise estimating the modulus of the exponential sum by means of the triangle inequality as provides a better bound.
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