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Thread: Can somebody explain the Riemann hypothesis?

  1. #1 Can somebody explain the Riemann hypothesis? 
    Forum Junior anticorncob28's Avatar
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    I just want a quick answer, I'll try to close this as soon as I get one. I'm just a little confused. The Riemann-Zeta function is defined as zeta(x) = 1 + 1/2^x + 1/3^x + 1/4^x. Originally I believed the Riemann hypothesis stated that if zeta(x) = 0 then x is a complex number with a real part of 0.5. This made sense to me. However they stated the "non-trivial" zeros, and then stated the trivial zeros were the negative even integers. However, for a negative even integer like -6, zeta(-6) = 1 + 1/(2^-6) + 1/(3^-6)... = 1 + 2^6 + 3^6 + 4^6..., how does this equal zero? Does this formula not apply to all values of x?


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    Forum Junior anticorncob28's Avatar
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    Nevermind, I figured it out with Ramanujan sums and methods to sum divergent series. If only I could find a way to delete this thread, or if somebody moves it to the trash...


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