Value-Distribution of the Riemann Zeta-Function along its Julia Lines

Abstract

For an arbitrary complex number $a\ne 0$ we consider the distribution of values of the Riemann zeta-function $\zeta$ at the $a$-points of the function $\Delta$ which appears in the functional equation $\zeta (s)=\Delta (s)\zeta (1-s)$. These $a$-points ${\delta }_a$ are clustered around the critical line $1/2+i\mathbb{R}$ which happens to be a Julia line for the essential singularity of $\zeta$ at infinity. We observe a remarkable average behaviour for the sequence of values $\zeta ({\delta }_a)$.

11 pages, dedicated to the Memory of Stephan Ruscheweyh

Cited by in corpus (2)

• Riemann-Type Functional Equations -- Julia Line and Counting Formulae --
• Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line