Functional equation and zeros on the critical line of the quadrilateral zeta function

Abstract

For $0<a\le 1/2$, we define the quadrilateral zeta function $Q(s,a)$ using the Hurwitz and periodic zeta functions and show that $Q(s,a)$ satisfies Riemann's functional equation studied by Hamburger, Heck and Knopp. Moreover, we prove that for any $0<a\le 1/2$, there exist positive constants $A(a)$ and $T_0(a)$ such that the number of zeros of the quadrilateral zeta function $Q(s,a)$ on the line segment from $1/2$ to $1/2+iT$ is greater than $A(a)T$ whenever $T\ge T_0(a)$.

18 pages. The abstract and structure are changed. Some typos are corrected. Some sentence are added and corrected

Cited by in corpus (1)

• On zeros of bilateral Hurwitz and periodic zeta and zeta star functions