Simple Zeros Of The Zeta Function

Abstract

This note studies the Laurent series of the inverse zeta function $1/\zeta (s)$ at any fixed nontrivial zero $\rho$ of the zeta function $\zeta (s)$, and its connection to the simplicity of the nontrivial zeros.

Nine Pages. Shorter Version. Keywords: Zeta Function, Nontrivial Zeros, Simple Zeros, Critical Line

References in corpus (10)

• Roots of the derivative of the Riemann zeta function and of characteristic polynomials
• On some reasons for doubting the Riemann hypothesis
• Partial sums of the M{ö}bius function
• On the multiplicity of zeros of the zeta-function
• Lower bounds for moments of zeta prime rho
• Note on Prime Gaps and Zero Spacings
• Simple zeros of degree 2 L-functions
• Linear relations of zeroes of the zeta-function
• The distribution of the summatory function of the Möbius function
• On the distribution of imaginary parts of zeros of the Riemann zeta function, II