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New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?
« on: 09/05/2024 10:19:13 »Quote
The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ(s) = 0 when s is one of −2, −4, −6, .... These are called its trivial zeros. The zeta function is also zero for other values of s, which are called nontrivial zeros.The equivalent statement for the trivial zero is:
The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that:
The real part of every nontrivial zero of the Riemann zeta function is 1/2
Thus, if the hypothesis is correct, all the nontrivial zeros lie on the critical line consisting of the complex numbers 1/2 + i t, where t is a real number and i is the imaginary unit.
https://en.wikipedia.org/wiki/Riemann_hypothesis
The imaginary part of every trivial zero of the Riemann zeta function is 0
The trivial zeros of the Riemann zeta function don't seem to attract much attention because they don't seem to be related to prime numbers. They don't seem to contain elements of "surprise".