%0 Journal Article %T Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value Theorem of Calculus %A Alfred W¨šnsche %J Advances in Pure Mathematics %P 972-1021 %@ 2160-0384 %D 2016 %I Scientific Research Publishing %R 10.4236/apm.2016.613074 %X

By the second mean-value theorem of calculus (Gauss-Bonnet theorem) we prove that the class of functions\"\" with an integral representation of the form \"\" with a real-valued function \"\"which is non-increasing and decreases in infinity more rapidly than any exponential functions \"\",\"\" possesses zeros only on the imaginary axis. The Riemann zeta function \"\" as it is known can be related to an entire function\"\" with the same non-trivial zeros as . Then after a trivial argument displacement\"\" we relate it to a function \"\" with a representation of the form \"\" where \"\" is rapidly decreasing in infinity and satisfies all requirements necessary for the given proof of the position of its zeros on the imaginary axis z=iy