The Mean Square of the Hurwitz Zeta-Function in Short Intervals
The Mean Square of the Hurwitz Zeta-Function in Short Intervals
The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter 0<α⩽1 is a generalization of the Riemann zeta-function ζ(s) (ζ(s,1)=ζ(s)) and was introduced at the end of the 19th century. The function ζ(s,α) plays an important role in investigations of the distribution of prime numbers in arithmetic progression and has applications in special …