The Generalized Riemann Hypothesis (RH Saga S1E3)

This is the third episode of the RH Saga.

We continue our journey by considering the zeros of L-functions beyond the Riemann zeta function. The location of these zeros is the subject of the generalized Riemann hypothesis. The story of these zeros also give a first indication of the general relationship between prime numbers and L-functions.

The overall aim of RH Saga Season 1 is to map the landscape of L-functions, as a foundation for future in-depth exploration of some of the most immortal math problems of all time.

This video is part of a PeakMath course. Join the journey at https://www.peakmath.org/

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Chapters:
00:00 - Intro
02:00 - Review of examples
05:04 - Analytic continuation
12:39 - Zeros in the critical strip
16:44 - Cosine waves
21:35 - Final remarks

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Links:

1. LMFDB
https://www.lmfdb.org/

2. "The Music of the Primes" on Amazon UK:
https://www.amazon.co.uk/Music-Primes...

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Errata:

The integral written at approx. 11:00 has a slight mistake. Instead of the number 2, the variable s should be used inside the sine function in the integrand. Correction displayed on screen at 11:20.

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Social:

https://www.peakmath.org/

#RiemannHypothesis #F1Geometry #Mathematics #PeakMath #RHSaga #Langlands