Scrolling graph of Riemann-Siegel Z(t) with sound effects

[ortega24024]

GREAT to hear from you Odin! I truly like hearing from you 100 times more than from many others who "know" me. Try calling again sometime: I am very busy sorting out all my mess (financial, social, computer... romantic even) and so sometimes am out (gardening, giving maths tuition, trying to get rifd of that stupid big guitar amplifier for my sis again, etc etc). I WILL check out all your videos eventually...and WILL (long overdue) upload some more myself. STAY POSITIVE!

[odinheim]

Hello Tim . I tried to call you

[ortega24024]

ANYONE READING THESE COMMENTS: I recommend skipping to the much older comments... plus try some of the channel comments I just put on my own profile page (in response to nickharvey7)... plus try some of the OLDEST channel comments (before they got lost in the noise of all the inane matey chat with random "friends"...most of whom requested me... not to mention: got lost in the noise of all the rock'n'roll mayhem).

[ortega24024]

@SaulHirschberger: It's ok (you alter ego)... I think the annotations just disappeared because of support waning out for this ancient computer (I can still see the annotations on the upstairs machine).

[ortega24024]

@SaulHirschberger :...and don't forget that it's ME who ALWAYS ends up editing the vids, restoring decorum and getting YOU out of YOUR icky little pickles (that nearly ALL the woosy humans (esp those with "power" or "money") like to whine about like the small girls that they are). ITWASALWAYSUPTOME...ANDIalways­GETeverythingRIGHTINTHEEND (unlike EVERYONE else): the more anyone tries to break me the stronger, calmer, genter, more patient, kind (yet careful and if necessary BRUTAL) I get...

[ortega24024]

@SaulHirschberger : WELL THANKYOU 4 THAT (sincerely)....but MIND YOUR MANNERS (CHILD)...and go easy with those sweet girls (FFS make sure they're OLD enough and stroke them more gently than a cat... THAT'S what heals them... I was doing all that back in '94 when you and all those revolting townies and rock kids that Nick lumbered you with were (and still are) pussying around like a bunch of little WOOSES): more to the point:THANKYOU YOUTUBE 4 SAVING ME A JOB (toning down my annotations)...

[SaulHirschberger]

ANNOTATIONS SOMEHOW HAVE VANISHED! GOOD JOB I ALWAYS HAVE MULTIPLE BACK-UP PLANS WITH EVERYTHING I DO THEN: lay your spirit down easy, ortega: ALL your annotations (complete with evidence for legal cases against known murderers and liars like Barclays and the British Empire) are safe with me. The a/c number was 80893323. The PIN was 7886. WHO REPORTED IT LOST OR STOLEN? DON'T answer (it is not my responsibility to work it out). FOODCOMES1stTHENMORALS.ALLbadg­uysLiKeIsraELswIlLsOoNbE NAILED.

[ortega24024]

The density function it looks like we are converging to at 2:55 is the Gaudin density, which was first described with a Fredholm determinant, and then using a solution to the Painleve V equation. This conjectured convergence is the Montgomery-Odlyzko law, coming from RMT.

RMT began with Wigner, Dyson et al early last century. In the 70s, Montgomery calculated the "pair-correlation function" of the zeros of the zeta function (on RH and the Hardy-Littlewood prime k-tuples conjecture)...

[ortega24024]

...to be 1-sinc^2 x. Montgomery showed this to Dyson at a coffee break, and Dyson explained this was the same as for eigenvalues (in the bulk of the spectrum) of random hermitian matrices from the Gaussian Unitary Ensemble. The random matrices correspond to random quantum hamiltonians modelling heavy nuclei. The upshot of all this is that the Riemann zeros seem to be behaving statistically rather like energy levels of nuclei, but before we get too excited Ian Stewart thinks that the proof...

[ortega24024]

...of RH (if it is true) will involve hitherto unknown connections with physics quite different than this. Sir Michael Berry (pioneer of quantum chaology) has used these ideas to speculate on the nature of the conjectured Hilbert-Polya operator whose existence would imply RH. Comparisons with Alaine Connes' ideas(non-commutative geometry) have been made. One of Berry's students was Jon Keating. He is leftmost on the conference picture at 2:24 . Next to him is Nina Snaith, and together...

[ortega24024]

they proved results on moments of characteristic polynomials of random matrices, and used this to formulate a conjecture on "moments of the zeta function". This earnt them a bottle of wine from Peter Sarnak. I met Sarnak in 2002, and it turned out he'd played squash with my uncle in Princeton. He invited me to a RH conference organised by him and (prover of Fermat's Last Theorem) Andrew Wiles, but I decided not to go because I couldn't afford it and thought it'd be over my head...

[ortega24024]

...I'm actually redoing my own check on (a later elaboration of) the Keating-Snaith conjecture right now. Rudnick (also on the conference picture) and Sarnak have proved unconditional results in the direction of Montgomery's original work. Katz and Sarnak have unconditionally shown that the RMT model all works for function field zeta functions. Berry and Keating created a smoothed version of the Riemann-Siegel formula (which I have also programmed) along with the Odlyzko Schonhage method...

[ortega24024]

...How much of all this do I understand?! Not the physics. A bit of the RMT. Montgomery's paper was easily digested, as was the B-K formula and O-S method. Keating took me to one side and showed me his resummation method to quickly derive R-S (I also made it work for Dirichlet L-functions and almost did it for zeta^2). Small world again: my old French teacher's son helped my dad's colleague write a recent RMT book (I went to his lecture about it - see "Nick's noughts and crosses...")...

[ortega24024]

...I corrected his statement of the Hardy-Ramanujan formula (easy) for the partition function (Dyson did work on partitions too). The same mangled version appears in Madan Lal Mehta's book.

At Oberwolfach, Keating said I was "a picture of tranquility" - 2 weeks later I had nervous exhaustion and didn't sleep for 5 days (also triggered by my 1st experience of marking and other stuff)! My uncle (a CFD guy) said I should've gone to the Sarnak-Wiles conference in NY anyway. OVER AND OUT!

[ortega24024]

...if you want more search "The Music of the Primes (6 of 6)"

[1nglewattz1]

I love it,

[ortega24024]

Hey - is that you, the Nigel Watt I mention in the description to "Perturbed cubic Gauss sums"?! If so, then congratulations on being a better student of Huxley's than me...and I've got a couple of funny stories about me+my dad mulling over your work! Last year Martin told me to see if I could fix Cappell and Shaneson's circle problem solution. I suppose I should click on you now to see if it really is you...

[ortega24024]

...Hmm. Wouldn't rule it out. If it is you then good to see you have a life out of maths. If not then you now know your name is rather similar to a maths guy who deserves more fame than many famous people (but the media and public are morons so the world doesn't work like that).

[ortega24024]

My voice is weird on this video because I'm stressed and feeling introspective!