I found these people online. They call themselves GONEK BAND
Hard to tell if there's any relation, since depending on where you travel, Gonek means either: porch/stoop, fire, or honey...
A tiny Gonek:
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A brief aside: I love the way number theory and literary theory sound so similar at times.
EX:
- Clusters of near-degenerate levels dominate negative moments of spectral determinants
On Small Distances Between Ordinates of Zeros of
(s) and '(s)
Proof that Overspecialization hasn't overtaken all fields:
"Limericks by Martin Huxley
[These describe the various lectures and discussions which took place at the 2002 Workshop on Zeta-functions and Associated Riemann Hypotheses at the Courant Institute in New York.]P. Sarnak - "L-Functions, operators and symmetry"
Tell the Riemann Hypothesis crew
That zeta alone will not do.
Precise applications
To nice situations
Require it for L-functions too.
The randomised matrices model
Looks like you hope some other bod'll
Compute all the means;
Com'natoric machines
Make the integrals rather a doddle.
Needing no fancy index or specs,
Keating measures cross-product effects.
Though no proof has been shown,
It fits all data known,
And it passes numerical checks.
The Eisenstein series of Maass,
Though the simplest of things in their class,
Give the funky equation
And (new information)
A threshold no zero can pass.
Paul Cohen, continuum hero,
Enquired of Piatecki-Shapiro,
"What functions will do
On adèles mod star Q?"
"Don't touch it! You want to find zero?"
With factors from every locality
Mixed up like a Florida ballot, he
Discovers it bearing
Symplectical pairing,
Thus questioning Connes's reality.
The Shnirel'man-Zelditch affair
Smooths out all the Maass function square,
Giving evidence more
For what Sarnak is sure:
No scarring or bumps anywhere.
S. Haran, "The mysteries of the real prime"
There were slides in the land of the Lord,
There's a book that we cannot afford.
Now the insights of Haran
No longer seem barren;
It's much better sense on the board.
Haran's work in the finitised case
Gives a proper orthogonal base.
To simulate Weil
In a positive way,
Write Wp as a trace.
The possible uses are teeming,
Surpassing so-called 'Parsan's dreaming'.
A sequence that halts
Leads to many results,
But not necessarily Riemann.
J. Lagarias, "A two-variable zeta function for number fields"
"Transparencies made late at nights
Should be read in a different light.
Please look at my slide
As a garrulous guide,
Who is not necessarily right."
The Riemann and Roch-ing connection
Appears on a closer inspection
Of the thesis of Tate
Not as something to state.
It is only the head of a section.
Pelikaan gave the clue what to do,
With an elegant function of two,
Counting weights in a code,
And his mates that he showed
It could generate L-functions too.
No continuous families? There's
The construction of Schoof-Van Der Geer's.
Should the zeros be fixed?
The parameter mixed
Them, exchanging positions in pairs.
B. Conrey, "L-functions and random matrix theory"
Brian Conrey has int'resting news
With Keating and Snaith and Chris Hughes:
The moments foreseen
Are confirmed by machine.
What is seen at the Number of Skewes?
Take zeta one half plus i T.
Is its modulus greater than V?
Can the size of the set
Be predictable, yet
You get root T in accuracy?
The values of zeta we see
Are an island of stability.
To topple our towers
Of forecasts for powers,
A storm of size root log log t.
H. Montgomery
Bombieri one year went to ground
To elucidate Chebyshev's bound.
His tale of endeavour
Was told to us never;
Apparently nothing was found.
'Polynomials don't do a lot'
Was the theme of Montgomery's slot.
"Best constants conjectured
Are those that you lectured?"
"I think so. The Borweins think not."
A. Odlyzko
With tricks that complete Riemann's hint
Odlyzko makes zeros a sprint.
One programming quirk
Keeps deleting his work:
You have to do SAVE before PRINT.
It's records, not theories, that fall,
Although ten to the fifty's a wall.
If you find a disproof,
(Sorry, Connes, Haran, Schoof!),
Then Clay will not pay you at all.
S. Gonek
The Levinson method, says Gonek,
Who's frequently somewhat sardonic,
Counts zeros as if
There's a one by log shift,
But the progress is not monotonic.
X. Li
De Branges' continued activity
Rearranges his proof. Will he give it? We
Are told by Li Xianjing,
His story's unchanging,
Though his range doesn't have positivity.
Gonek & Miller
Four zeros bad - what information?
Is it curtains for pair correlation?
A factor to fiddle
Can go in the middle,
So the riddle was not devastation.
N. Katz, "The importance of family values"
If Weil had not lost in the Crash,
And retreated to maths to earn cash,
He would rise to high rank
As the head of a bank
And perhaps win the Prize, and not Nash.
The method that Katz wants to give
Renders all that's symplectical triv',
And integer values
At the powers we shall use
Makes it clear where the poles have to live.
What made Grothendieck terribly good
Was, he can't see the tree for the wood.
He aimed to surpass
Andre Weil and his class,
And he beat whomsoever he could.
I. Fesenko, "Analysis on an arithmetic scheme and the functional equation of its zeta function"
The viewpoint in days such as these
Is to not see the wood for the trees,
As the dog by its habit
Cannot see the rabbit,
Nor its infinitesimal fleas.
The local p-adic fields (bless 'em all!)
Have a grading that's infinitesimal.
But to see higher rank,
What was localised shrank
To the point it was infinitesimal.
The new thing Fesenko can try:
To complete the point x at point y.
He completes y at x
With the self-same effects,
Getting fibre relations thereby.
C. Deninger, "Elliptic curves over finite fields and transversal index theory"
Said Deninger, mathematician,
"It's transverse in Lie or position.
Suspicion won't do.
This clearly is true,
Even if you don't know definition!"
For a new topological space,
Take division point lattice as base,
Make it 3D as well,
Quotient down to a cell,
And you're into the solenoid case.
H. Iwaniec, "Modular approximations to the Möbius function"
With some interruptions and fuss,
Iwaniec presented to us
A conditional bound
For the class number found,
But technic'ly hard to discuss.
Iwaniec's new programme guides
Where the Siegel exceptional hides;
A sort of Big Brother:
One angle or other,
We watch it from so many sides.
Shouldn't lectures speeding face fines?
For I have to take notes missing lines.
The result was terrific,
But my scrawl hieroglyphic:
"Theorem. m not exceeding five nines."
E. Lapid, "L-functions and root numbers at the center of symmetry"
Getting L-functions greater than nought
Requires special values be caught
As factors upstairs
With symmetrical squares
Whose continuance has to be fought.
The positive values of Lapid
Make delivery terribly rapid.
When he scrolled on his laptop
The wall image snapped up,
Left me feeling all sea-sick and vapid.
J. Keating
Under gravity, gas in a ball.
Do the free oscillations stay small?
The stable condition:
First order Hermitian,
And Riemann discovered it all.
If Riemann had spoken his heart,
We would have Polyá's clue from the start.
His manuscript revels
In energy levels,
Then zeta is taken apart.
M. Balazard
A fraction-part functional space,
Is a step-function spanned by the base?
For n-widths they find
Asymptotics refined,
With a lower bound proved in its place.
J.-F. Burnol, "From Riemann sums to Riemann zeros: challenges above and beyond the Fourier Transform"
The construction that Burnol prepared
Has the wave-functions boldly declared
Contractions amassed
Span the log? Not so fast,
When you count multiplicity squared.
A. Deitmar
When Deitmar was occupied solely
With compactified spec and its coh'ly
He woke in the night,
Knowing all was alright:
He dreampt Germany picked him as goalie.
Hyperbolical flow is essential
To get zeta as det(differential).
When Deitmar in slumbers
Saw spec of whole numbers,
He awoke and reduced to tangential.
Is the Riemann Hypothesis deep?
It made Hardy and Littlewood weep.
Or is there a trick
Gets the answer so quick
That Deitmar could see in his sleep?
C. Newman, "Zeros of Ising model partition functions: What Lee and Yang did not win their Nobel Prize for"
The New Man for Courant Director
Followed Old Man Polyá in his lecture.
A lattice with links
Leads to zeta, he thinks,
And he knew how to work the projector.
The transform of xi is a density
With twice exponential intensity.
The resemblance is teasing
To the model of Ising,
With its definite line-up propensity.
The link with the model of Ising
Is one of those things that is teasing.
Distribution that's joint
Is a critical point:
Is it vapour, subliming, or freezing?
Ideas that Newman now floats
Are released from his twelve-year-old notes.
Probabilities dense
Should give zeta, and thence
Lee and Yang harvest Riemann's wild oats.
M. Zirnbauer
For Lie group analysis there's
A concept that's nice: dual pairs.
With this information
A representation
Gives characters up- and down-stairs.
Do Haar measure structures allow
Taking means on a group? They do now.
And even beginners
Can oscillate spinors,
As Zirnbauer will show you Howe.
S. Cappell, "Counting lattice points"
He impressed us at Luminy - very,
Did Sylvain Cappell in a beret.
From algebra comes
The rule to find sums.
It it gets written up we'll be merry.
Cappell says Todd class in the Chow ring
Is algebra's Euler-Maclaurin.
His lecture near shrank
When the next slide was blank,
But he managed to shovel some more in.
D. Goldfeld, "Moments of zeta functions"
The series that Goldfeld has shown
Continue to critical zone
Give moments of zeta,
But no record-beater;
They're cases where moments are known.
How moments of zeta to force?
Take multiple s's of course.
A life of great ease?
No, it's moments like these
That cost you a life of remorse.
A method that makes moments sweeter,
Continuing multiple zeta.
A student called Meera
Has got a lot nearer;
Non-classical cases defeat her.
Persuading high pow'rs to unwrap
Takes a multiple sum, not a scrap.
Continue it far,
Past the poles where they are,
And the moment falls into your lap.
L. Weng, "New non-Abelian zeta functions"
Lin Weng's new construction immense:
Definitions were left in suspense,
With micro-locality,
Top group duality,
"Whenever the counting makes sense."
The construction Lin Weng carries through
Has a product of sorts in rank two.
Should you call it a zeta?
Related to theta,
For Q in rank two it's still new.
B. Duke
With the Riemann Hypothesis found,
We would have a nice quantity bound.
Any quality fruits?
Only primitive roots.
Has a summit been reached or a mound?
R. Murty
Ram Murty discussed sub-convexity,
Not just something where it expects to be,
A structure's required
To get what's desired,
And the proofs have a certain complexity.
A. Perelli
Can Selberg's five-axiom class
Beyond automorphic ones pass?
And how many twists
Before there exists
A rho, holomorphic or Maass?
P. Michel, "On the sign of Kloosterman sums"
An oracle there to appeal,
But the field must be totally real,
So ternary quadrics
No longer play odd ticks,
As Sarnak and friends can reveal.
Rank two with a level inflation,
It starts with an amplification.
First trick to take place
Is the Petersson trace
Followed by "Voroino summation".
After nearly an hour of tension,
The crucial point got in a mention:
A determinant mean,
"As also Deligne,
Recurrence of rank of dimension."
H. Stark
The zero permitted by Siegel
Is setting itself up as regal.
It leads a procession
Around its possession.
Can such a behaviour be legal?
Stark noticed a property strong:
Sum of cosines is negative long.
If this cannot be,
Then improvement we see
On the line where no zeros belong.
M. Huxley
Still Huxley is puzzling through
A method that's now not so new.
Large zetas are seen
Through a fourth or fifth mean,
And fourth powers bring SL two.
J.-F. Burnol
If support misses nought and infinity,
Both Poisson, Co-Poisson come in it. He
Follow De Branges
With transforms whose range is
Pairs zero at nought and infinity.
The functions considered by Burnol,
Their support on the line is internal,
And the mapping that shows
Taylor series at rho's
Is eigen with suitable kernel.
B. Julia, "More arithmetic groups in (theoretical) physics"
The formalised Hilbert was blessed
By Cantor, the infinitist.
Must Julia dim it?
"The classical limit,
Like Paradise, doesn't exist!"
Say physicists, whom we should venerate,
In eleven dimensions, at any rate,
With rusting away,
The beauties decay,
With symmetries going degenerate.
K. Soundararajan
What problems remain at the end?
Success in detecting a trend?
The list that we found,
Presented by Sound'
Consists of the usual blend."
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PROOF THAT THEORY ISN'T DEAD:
"Emerging Applications of Number Theory
Summary
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Click here for soviet deportations of Polish Nationals snippets.
(why, you ask? Well how should I know? You're the one with the fingers of will or won't)
It has some letters from dead Goneks.
I would copy and paste it here, but apparently, they are so fervently against deportation, they won't even permit their text to travel....So much for inheritance...we no longer have the right to directly share the words of our own ancestors. I wonder if they could actually prosecute for that....
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A woman of valor, | By | New Yorker "rayk4" (New York, NY USA) - See all my reviews |
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1 comment:
i miss you lovely lady. i hope we will meet again in waking very soon.
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