Скачать или смотреть Invariants and Millennium Problems (RH Saga S1E6)

This is the sixth episode of the RH Saga

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Continuing from the last episode, we now consider "invariants", i.e. machines taking L-functions as input and giving a number as output. These invariants are intimately connected to several Millennium Problems.

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

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Chapters:
00:00 - Intro
03:16 - First examples
11:36 - Keiper-Li coefficients
18:04 - Structure
26:42 - Millennium problems
32:26 - Duality
36:02 - Final remarks

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Links:

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

2. LMFDB, Ramanujan Delta:
https://www.lmfdb.org/L/2/1/1.1/c11/0/0

3. LMFDB, Elliptic curve conductors less than 100:
https://www.lmfdb.org/EllipticCurve/Q...

4. "Riemann's Hypothesis" - Brian Conrey:
https://tinyurl.com/conrey90

5. SageMathCell permalink for Keiper-Li coefficients of K:
https://sagecell.sagemath.org/?z=eJxd...

6. Fungrim entry on Keiper-Li coefficients:
https://fungrim.org/topic/Keiper-Li_c...

7. Paper by Farmer, Pitale, Ryan and Schmidt on L-function axioms:
https://arxiv.org/pdf/1711.10375.pdf

8. Andrew Droll thesis pdf:
https://qspace.library.queensu.ca/ser...

9. Donald Yau, "Lambda-rings":
https://www.worldscientific.com/world...

10. Lindsay N. Childs, "A Concrete Introduction to Higher Algebra", Second edition:
https://link.springer.com/book/10.100...
(There is also a new third edition, which may be less expensive)

11. Mícheál Ó Searcóid, "Elements of Abstract Analysis":
https://www.amazon.com/Elements-Abstr...

12. Allen Hatcher, "Topology of Numbers":
https://pi.math.cornell.edu/~hatcher/...

13. The Millennium Problems:
https://www.claymath.org/millennium-p...

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Errata:

No errors found yet.


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