Both real and imaginary parts of the function F(s)=zeta(s)*Gamma(s/2)*pi**(-s/2)=xi(s)/(s*(s-1)), whose zeroes exactly coincide with the non-trivial zeroes of the Riemann zeta-function, have infinitely many zeroes for any value of Re(s)

2010/06/02 by S. K. Sekatskii, Sekatskii, S. K.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1007.0926

arxiv created 2010/06/02 · arxiv updated 2010/07/07

Abstract

The following theorem is proven: Both real and imaginary parts of the function F(s) defined as F(s)=zeta(s)*Gamma(s/2)*pi**(-s/2)=xi(s)/(s*(s-1)), and whose zeroes exactly coincide with the non-trivial zeroes of the Riemann zeta-function, have infinitely many zeroes for any value of Re(s).

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