8 thoughts on “Equivalent form of the Riemann hypothesis

  1. Here’s another one. Let H_n be the nth harmonic number (sum of 1/k for k=1 to n). That the sum of the divisors of n is less than or equal to H_n + exp(H_n)·ln(H_n) for any n is equivalent to RH according to this paper.

    It almost makes the problem seem approachable! But experts say there is NO WAY anyone’s going to get to RH via this route.

  2. John John Deragon

    By the way, in Princeton book, the statement is cited as

    |log(lcm[1, 2, . . . , N]) − N|  < √N (log N)^2.

  3. Slow to comment here, but let me put in a plug for a book I enjoyed tremendously. It’s called Prime Obsession, and it’s by John Derbyshire. Chapters alternate between (a) historical and biographical discussion of Riemann, and (b) a mathematical development of the Riemann Hypothesis, its antecedents, and some insight into why it’s so interesting and important. Derbyshire’s goal was to present the Riemann Hypothesis in a way that anyone with basic high school algebra skills could follow it. He almost succeeded; there’s a tiny bit of calculus at the end. For readers of this blog, though, all of the math is elementary.

  4. Please, look at Mochizuki’s recently updated paper,
    ” Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations ” .
    He added “Remark 2.2.1.” pp.46 .
    It seems to me that, perhaps, he is going to make a “double-play”, ABC conj and RH.

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