Distribution of absolute values of incomplete Gaussian sums (Q1851534)

The author considers an incomplete Gaussian sum of the form \(S_h(x) = \sum_{n=x+1}^{x+h} \chi(n)\cdot e^{(2\pi i an)/p}\), where \(p\) is a simple number, \((a,p)=1\), \( x\) and \(h\) are integers with \(0\leq x<p\) and \(0<h<p\), and \(\chi(n)\) is a complex character by modulo \(p\). The author establishes that the square modulus of this sum has asymptotically representative distribution.