Special values of L-functions (RH Saga S1E9)

[@tomkerruish2982]

I'm so glad you're still around. I was concerned.

[@artemetra3262]

babe wake up new peakmath has dropped

[@1.4142]

This channel should be called global maximum math

[@shorznmoor8127]

We have no reason to expect you to continue releasing this content Andreas, but I certainly hope that you will do so. The presentation is absorbing and your dedication and enthusiasm is very much appreciated. I speak as one who should really have no interest in such esoteric subject matter given that technically, I am mathematically illiterate, but the PeakMath project is illuminating. Good luck, and thank you.

[@SimonH1111]

Oh man. I just discovered your videos and they've totally rekindled my love of maths. I was sad to see that you couldn't make tye courseware financially viable. I hope you find a way to bring the Langlands Program to the mathematical masses another way.

[@colinbrash]

Please please keep doing this series. It has rekindled my excitement about math, and I hope it may excite my child as well when they are old enough. You are making such deep beauty available to so many.

[@tristen7823]

Finaly, I have been checking this Channel almost every day to check for new videos!!

[@amritawasthi7030]

The most lovely part is that whenever you drop a new video, i first watch all the previous ones to actually relate to it since you post after a long gap. It helps me revise the same. Thank you. The content is one of its kind.

[@chatchawanpanraksa]

I hit thumb up even before watching the video. Then watched it twice. Well done sir. Many thanks!

[@АндрейВоинков-е9п]

So long.. I have to start it over when new episode ready

[@АндрейВоинков-е9п]

BTW I already watched every episode 2-3 times

[@MichaelMaths_]

@@АндрейВоинков-е9пReal. What else were we going to do with the extra time anyways?

[@sahhaf1234]

So happy to see you back... Pls continue with these videos..

[@graf_paper]

Your back, in am rearranging my evening plans for this!!

[@missoss]

I just saw the website has closed down. Please keep publishing this type of content! Thank you.

[@Higor-bx2my]

This project is wonderful. I hope it continues for many seasons.

[@psycdalex]

Its been so long. Im so glad this is still going❤

[@alexnagle575]

Being able to concisely describe incredibly complex topics in an understandable and entertaining format is the mark of true genius, my hat is off to you sir for all of these videos.

[@debingzhang522]

Oh, these videos are truly awesome, the best math I have ever seen. And I also wonder if something I can do to help create more such videos.

[@MiroslawHorbal]

Glad there are more episodes. This has been an exciting topic to think about.

[@graptemys4186]

Thank you so much for continuing this fabulous series.

[@EdwinSteiner]

I'm so happy that the saga continues! Also, that was quite the teaser for the next episode! Very much looking forward to that!

[@Axacqk]

I wonder if you noticed a spike in the watch numbers of your past episodes. I certainly plan to rewatch from the beginning over the next week.

[@scottaitken549]

Great to see you again! Very informative, well done series. Looking forward to more

[@KStarGamer_]

So glad to see you back!

[@airfluxe2095]

Thanks for another amazing video

[@leflipPhil]

Bravo continuez autant que vous le pouvez et merci infiniment

[@cosmicwakes6443]

Thank you.

[@АндрейВоинков-е9п]

Imagine Mochizuki explained his work in such series

[@VaradMahashabde]

Peak has returned

[@bdi7518]

could wait for the next episode

[@sahhaf1234]

Thank you very much.

[@AvanaVana]

…finally!!! 😮

[@humblepride1023]

After half a year of waiting we can finally learn a new episode. Thank you.

[@easymathematik]

There is such a big secret behind all this stuff. I will not be on this planet anymore to see all this beautiful diamonds.

[@psycdalex]

We can hope. I want little more than to be alive when the Riemann hypothesis is no longer a hypothesis.

[@easymathematik]

@@psycdalex My hope is that Peakmath has a big surprise. The way he talks is not just explaining RH. The hidden sound in his voice scares me little bit. In a positive meaning. :D

[@psycdalex]

@@easymathematik i hope you're right. This series is the best.

[@easymathematik]

@@psycdalex True. No words needed.

[@DeathSugar]

so finally you've become alive after the recent new formula. are there any estimates on it ?

[@brkhuwang6293]

It feels like decades...

[@YouTube_username_not_found]

What's the best way to compute hexadecimals of pi? Answer: Bailey-Borwein-Plouffe formula

[@TheSummoner]

The intro music is a bit ominous, almost David-Lynch-style 😆 Edit: Mascheroni is pronounced with a hard C sound, like it was written Maskeroni

[@tomkerruish2982]

Oily macaroni constant.😅

[@GrahamGarnerQu]

I think the music is generated in some way from L-functions....

[@wojtech6221]

Excellent!!!

[@nathanisbored]

It just occurred to me that our main characters P, E, A, and K spell out peak (peak math?)

[@tapir1073]

Saved my day!

[@matt9455]

thanks for making more videos! these are inspiring. is there a theory for special values of L-functions involving j-invariants of ECs? transpositions of non-conjugate zeros of the Riemann zeta function in the critical strip seem bounded by ECs with 1/2 as a rational point

[@KStarGamer_]

Not in terms of j-invariants but there is a conjectured expression for L(E, n) for n >= 3 (for n=2 we have Bloch’s conjecture) that can be found in Goncharov’s paper on polylogarithms in arithmetic and geometry as conjecture 0.10. At n=1, we have formulae for rank 0 and rank 1 L-functions and refined BSD conjectures the expression for all ranks.

[@matt9455]

​@@KStarGamer_ wow thank you! I wish i knew more about elliptic curves, i'm definitely going to finish that paper. in 0.11 for the n=4 case, could we use the modularity theorem and Bloch's conjecture to express the coefficients of L(E,4) in terms of the coefficients of L(E,2)?

[@KStarGamer_]

@@matt9455 I'm not too sure on the proof but that seems potentially reasonable

[@sonarbangla8711]

Very interesting, however is there a monograph explaining RH Saga?

[@adamnealis]

Where have you been? I have missed your video lessons.

[@psycdalex]

Around calculus i really started to love the beauty of math, then it started to lose its luster a bit as the topics became less mindbending and mysterious. At the peak however, the beauty is back.

[@benovision6325]

Is it possible to generate an infinite series of integers which are not prime, and excluding series made from even numbers or powers of numbers?

[@Higor-bx2my]

What would be the p adic L functions and Heegner points?

[@rainbow-cl4rk]

At 13:00 I don't get how [0,1]³ can be expressed as P(x,y,z)>0

[@SIXSHAMAN]

If I only have Dirichlet series, how can I find the corresponding L-function in LMFDB? I don't know the degree, the conductor, etc. I don't know how to compute these. What can I do?

[@fragilelys]

beautiful..

[@KhalidMatan-o2k]

Finally

[@wojtech6221]

I can't stop my satisfaction!

[@PedroFigueiredo-q9x]

Zeta (-1) =-1/12 is misleadingly called " SUM of all natural numbers". And the venerable, classic Greek letter pi is pronounced as pea, not as pie by confused minds.

[@quarkonium3795]

I agree about -1/12 but strongly disagree about pea vs pie. "Pea" is how it is pronounced in greek, but "Pie" has become the commonly accepted pronunciation in English-speaking countries and media. Imagine how confusing math and physics lectures would be if they constantly had to distinguish between the letter "p" and the number "pi", especially when "p" is sometimes used as a variable. There's room for discussion when it comes to symbols like "phi" which I've heard pronounced as "phee" or "phie" by different professors, but I've never heard a single english-speaking academic professional use "pea" as the pronunciation for pi eve though it's technically the original pronunciation

[@PedroFigueiredo-q9x]

Thanks for the thougtful elucidation. In natural science standardization is law, a meter is the same in every language and pronounced similarly. Why should the popular English pronounciation be odd ? Vox populi vox dei ?@@quarkonium3795

[@RiotSociety666]

😂😂😂