A new problem equivalent to the RH - submission/peer-review

[Thomas JR.]

Hello,

This paper needs peer-reviewing. I know for sure that the results are

correct because I've tested them exhaustively on Mathematica.

This new paper has been submitted to arXiv, and am looking for a little

publicizing of the new function presented, phi(k), which is a "cousin" of the Zeta function, zeta(k).

This new function shares the same non-trivial roots with the zeta function, but it doesn't share the trivial roots (zeta has the negative even integers as trivial zeros, this new function has the positive odd integers as trivial zeros, and also the trivial zeros of the eta function, which are 1+2*Pi*i*j/Log(2), for j integer, as trivial zeros).

Function phi(k) relates to the zeta function through a functional equation which is a little similar to Riemann's functional equation, but it differs in a few ways (cosine instead of sine, etc.) Well, read the paper and you will know.

This paper doesn't solve the RH, it just presents some new results, the most striking of them being the existence of this cousin function, which seems to not have a pole.

https://www.researchgate.net/publication/346552243_A_new_approach_to_the_Riemann_hypothesis