Hisashi Kobayashi's Blog

Sherman Fairchild University Professor Emeritus of Electrical Engineering and Computer Science, Princeton University

Towards a Proof of the Riemann Hypothesis (RH)

December 20th, 2016

RiemannI shall report in a series of articles my investigation on the famous 150 years old conjecture made by Bernhard Riemann (1826-1866) in 1859. The purposes of the reports are threefold: First, this writing effort will force me to study thoroughly prior arts on this subject, which should help my research towards a possible proof of the Riemann hypothesis (RH). Second, when I submit new results to mathematical journals and/or post them on arXiv (an online publication website) , I can refer to these articles on my website as for the background information, which will allow my journal paper(s) to be more concise than would be, otherwise. Third, if I am successful in compiling prior arts and my own results in a cohesive manner, this series of articles will serve as core materials for a book or monograph.

Furthermore, I hope that this series will stimulate some readers and make them interested in this fascinating and profound subject.

No. 1: Euler’s zeta function
No. 2: Riemann’s zeta function and the Riemann hypothesis
No. 3: Riemann’s xi function and the product form representation
No. 4: The Fourier transform representation of the xi function
No. 5: Some results on the ξ(s) and Ξ(t) functions associated with Riemann’s ζ(s) function
No. 6: Local Extrema of the Ξ(t) Function and The Riemann Hypothesis
No. 7: The Z(t) function, Gram’s Law, Riemann-von Mangoldt Formula, and Lehmer’s Phenomenon
No. 8: Negativity of d2/dt2 logΞ(t) and a conjecture on a sufficient condition for the Riemann hypothesis
No. 9: Application of the Euler-Maclaurin summation to log-differentials of M(t) = |ζ(1/2 + it)|

Hisashi Kobayashi
December 20, 2016


Leonhard Euler (1707-1783) Source: Wikipedia

Carl Friedrich Gauss (1777-1855) Source: Wikipedia

Carl Friedrich Gauss (1777-1855)
Source: Wikipedia

Lecture Slides of Probability, Random Processes and Statistical Analysis

December 20th, 2013

I am currently teaching a graduate course “ELE 525: Random Processes in Information Systems” at Princeton University on Mondays and Wednesdays in the Fall Semester 2013-14. I taught the same course in the Fall 2012-13. I post here the lecture slides, hoping that they will be useful to other instructors who will teach similar courses. The slides should be also useful to those who wish to study the subjects based on the textbook Probability, Random Processes and Statistical Analysis, by Hisashi Kobayashi, Brian L. Mark and William Turin (Cambridge University Press, 2012, 800 pages).

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December 20th, 2013

プリンストン大学   小林久志Kobayashi

本記事は電気学会誌125周年記念特集 号(2014年4月発行)に掲載されたものである。

  1. はじめに
  2. 大学の国際化
  3. 「大学院教授」を廃止し学部教育を充実せよ
  4. 柔軟な教育に対する日米の差
  5. 飛び進学が英才教育か?
  6. 教育界の革命児ムークス