[math-fun] about arguments with the zeta function
Hello, I have foundsomething which could interest a few people, it is about the function 1/Pi*argument(Zeta(1/2+I*n)) and 1/Pi*GAMMA(1/4+I*n/2)), these functions appear in the context of the counting formula of Backlundwhich is (it does count the number of zeros of the zeta function). Z(n) = n/(2*Pi)*log(n/(2*Pi*exp(1))+ 11/8 + 1/Pi*argument(Zeta(1/2+I*n)). The unknown so far was that this particular Zeta with the argument is quite chaotic, well , it is still the same but I have found a general formula for it as well as one for the gamma function. The formula is quite simple, is uses [ ] and { }, the floor and fractional part of a number (or function)and Pi, log(Pi), log(2) and log(p) where p is a prime number. That kind of formula as far as I know was conjectured once by a certain Freeman Dyson, and some others as well like M.V. Berry, Connes, Hugh Montgomery , relating quasi-crystals to the zeta function. Well, that's one step for it. I think that mr Dyson was right. The article was submitted to certain friends and on the arxiv site, the abstract is in english and french and the article is in ... : french, YES, I know manyof you do NOT speak that language of Molière and the 'mot de Cambronne' will come to their mouth, I intend to think about it and make a serious effortfor it in the next few days, http://www.plouffe.fr/simon/On%20the%20values%20of%20the%20functions%20zeta%... the article is also in Word, yes the vulgar Word : http://www.plouffe.fr/simon/On%20the%20values%20of%20the%20functions%20zeta%... I have been working for this in the past 2 years. Here are the results, Best regards to all. Simon Plouffe/ /
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Simon Plouffe