Turán's method

In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution.

The method applies to sums of the form

${\displaystyle s_{\nu }=\sum _{n=1}^{N}b_{n}z_{n}^{\nu }\ }$

where the b and z are complex numbers and ν runs over a range of integers. There are two main results, depending on the size of the complex numbers z.