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

2019/10/22 by Takashi Nakamura, Nakamura, Takashi
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1910.09837

Abstract

For 0 < a ≤ 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 ≤ 1/2, there exist positive constants A(a) and T₀(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 ≥ T₀(a).

Related

• Zeros and the functional equation of the quadrilateral zeta function
• On Lerch's formula and zeros of the quadrilateral zeta function
• Notes on the Zeros of Riemann's Zeta Function
• An investigation of the non-trivial zeros of the Riemann zeta function
• All of zeros of Riemann's Zeta-Function are on σ=1/2