AUTHOR(S): Daniele Lattanzi

TITLE Elementary Proof of Riemann’s Hypothesis by the Modified Chisquare Function 
KEYWORDS Riemann’s hypothesis, modified chisquare function, numeric progressions 
ABSTRACT The present article shows a proof of Riemann’s Hypothesis (RH) which is both general (i.e. valid for all the nontrivial zeroes of the zeta function) and elementary (that is not using the theory of the complex functions) in which the real constant s=+1/2 arises by itself and automatically. The modified chisquare function in one of its four forms (±1/·)Xk^2(O,x/?) is used as an interpolating function of the progressions {n±a}, of their summations {Sn±a} and of the progressions {N±a+1/(±a+1)}, with a?R n,N?N so that k=2±2a and in the real plane (a,k) two halflines are set up with k<2. The use of the EulerMacLaurin formula with the onetoone correspondence between the summation operation S and the shift vector operator S=(Sa,Sk) in the real 2D plane (a,k) lead to find the zeroes of Euler’s function. Finally, the extrusion to the third imaginary axis it leads to prove Riemann’s hypothesis. 
Cite this paper Daniele Lattanzi. (2017) Elementary Proof of Riemann’s Hypothesis by the Modified Chisquare Function. International Journal of Mathematical and Computational Methods, 2, 612 