I would like to know what are the mathematical reasons for which Bernhard Riemann believed that his hypothesis is true, and I would like to know if those mathematical reasons were cited in his original paper.

My question Here : Are there papers or books or links that explain why Bernhard Riemann believed that his hypothesis is true?

Note: I do not want to know if the Riemann Hypothesis is true or false.

Thank you for any help

  • $\begingroup$ mathworld.wolfram.com/RiemannHypothesis.html In paragraph 4 it is discussed how Riemann developed the hypothesis, they reference a book in it that may help you answer your question. Cheers! $\endgroup$ – Dunka Aug 1 '15 at 0:01
  • $\begingroup$ I checked your link paragaraph 4, it's seems a standard information at all, and not show why he believed it is true .The problem in all paper concerned his hypothesis started always with his H. and never informed us at a least why he is believed it is true . $\endgroup$ – zeraoulia rafik Aug 1 '15 at 0:15
  • $\begingroup$ and also his believe why it is true is the almost proof of RH $\endgroup$ – zeraoulia rafik Aug 1 '15 at 0:22
  • $\begingroup$ Riemann was also inspired by Euler's work on $\zeta(s)$. If you search for "History of RH", there are several interesting papers. $\endgroup$ – Dietrich Burde Aug 1 '15 at 8:58
  • 3
    $\begingroup$ In short, Riemann did compute the first three zeros by means of what's now known as the Riemann-Siegel formula, as it was rediscovered only years later. Why that was sufficient for his conjecture, is questionable, it's probably more a matter of intuition than anything else. $\endgroup$ – Markus Shepherd Aug 1 '15 at 12:07

Harold Edwards provides some informed speculation on this question in his book. I'm not home right now but will come back and summarize his thoughts in a couple days.

And by the way his book is a gem. It includes a translation of the original paper, and one of the more enjoyable and satisfying couple months of my "mathematical life" was spent working my way carefully through that paper ( it invites lots of side-trips and explorations along the way... I had a particularly long sidetrack with the gamma function... )

  • $\begingroup$ I think you mean Harold Edwards, Riemann's Zeta Function? amazon.com/Riemanns-Zeta-Function-Harold-Edwards/dp/0486417409 $\endgroup$ – Bungo Nov 10 '15 at 3:15
  • $\begingroup$ yes, thank you very much. I don't know what I was thinking. Dover published the version I have. I changed my comment so future readers don't get misled. Thanks again. $\endgroup$ – Mathhead Nov 10 '15 at 3:19

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