Introduction to analytic number theory 13: Riemann-von Mangoldt explicit formula

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Lecture 13 of my graduate course, Introduction to analytic number theory, at the University of Western Ontario, May-June 2023.
01:45 Euler's estimation of zeta (2) via dilogarithm function
39:10 Von Mangoldt function
50:05 Riemann-von Mangoldt explicit formula
1:02:05 Perron's formula
  1. Masoud Khalkhali
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Комментарии
Автор

This was an amazing lecture. Thank you so much for posting.

FireSermon
Автор

Nice lecture, thanks. I miss something about the relation between the Hadamard infinite product and being able to sum over zeros in the integral that obtains the terms in the explicit formula through the residue theorem. I think it is important to have the zeta function in terms of an entire function and thus the product that allows the infinite sum of zeros in the formula in order to understand the whole picture.

adolf