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On an inequality for the Riemann zeta-function in the critical strip
Riemann zeta-function size of the Riemann zeta-function new inequalities critical strip
2012/6/30
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we est...
Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis
Mellin transform Riemann zeta-function Kontorovich-Lebedev transform modified Bessel functions Lambert transform
2012/6/21
We consider integral and series transformations, which are associated with Ramanujan's identities, involving various arithmetic functions and a ratio of products of Riemann's zeta functions of differe...