Paper Withdrawn: A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

The author has found today an error in the denominator of the residue equation (4.5). This unfortunate mistake makes the conclusions and the title of the paper incorrect. The function $Z(s,x)$ is regular at $x=1$ and the multivalued part disappears. The original motivation of the paper was to derive an old (and correct!) result due to the author using a different approach.

Mots clés: Number Theory; Riemann Zeta function; Polylogarithm function; Riemann nontrivial zeros

Domaines: Théorie des nombres [math.NT]

Lazhar Fekih-Ahmed. Paper Withdrawn: A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function. 2012. ⟨hal-00693281v2⟩