Rapport sur la conférence, par Martin Huxley.
How slowly do class numbers grow ?
We look for a bound from below.
There's still no prospect of
Making Siegel effective;
It's pathetic how little we know.
[On Iwaniec's talk]How smart number theorist are we
Who can use the lacunarity
To get at the zeros
That physicist heros
With randomised matrix can't see !
[On Iwaniec's talk]
The Dedekind zetas will do,
If these are lacunary too,
A simple solution:
The main contribution
Should come from the n close to the Q.
[On Iwaniec's talk]Slow class numbers grow is the mission,
Depending on zero's position.
The new implication
Fits pair correlation,
But there's no hope to prove the condition.
[On Iwaniec's talk]
It's fast, it's in french, my sight's poor,
And I'm certain that Fouvry said more,
But I'm sure that he comes
To small Salié sums
For a prime leaving residue four.
[On Fouvry's talk]In the theorems that Fouvry can give,
When he wants a conclusion non-triv,
Using Weyl with a Y
And then Weil with an I,
Then he can't get away from the Sieve.
[On Fouvry's talk]
Cojocaru's determined to show
Where the cyclic reductions should go:
A finite proportion
Are free of q-torsion.
Does she use modularity ? No.
[On Cojocaru's talk]For Nicolas speaking at Lille
This problem is not a big deal.
"It isn't a struggle,
You just have to juggle !"
Now ride on a bike with one wheel !
[On Nicolas's talk]
Where Sathe with great effort comes
For Selberg was just simple sums.
And so it shall be so
In séminaire Pisot,
While Delange's machinery hums.
[On Nicolas's talk]Nicolas, when he takes to the floor,
Can settle three problems or more.
It somehow compares
With sums of two squares,
Mod seven replaces mod four.
[On Nicolas's talk]
The fourth power mean needs dissection
And the smoothing and sieves and reflection,
And Virtanen picks
The pertinent tricks
To make the un-smoothing correction.
[On Virtanen's talk]For the moment of character sums
(With a sieve and a weight it all comes),
Removing the smoothing
In proving the new thing
Had the audience biting their thumbs.
[On Virtanen's talk]
In the diagram Matti would share
With connections that go here and there,
There's no arrow to pass
Direct from Laplace
To the error term in the mean square.
[On Jutila's talk]The function called Zed sub two
Is not quite so easy to do.
If the growth you would see,
You smooth over t;
Voronoi and Kuznietsov are due.
[On Jutila's talk]
We greatly desire to be thought of
A method that works at three quarters.
Whilst improving the theories
Of Dirichlet series,
It would make Ivic' lecture no shorter.
[On Ivic's talk]Take new-forms whose level N climbs,
Count zeros each so many times,
That's the theorem of Luo
And a popular duo;
Royer fixes the number of primes.
[On Royer's talk]
Will a smooth distribution prevail ?
There's a Lie at the heart of this tale ...
Be careful ! For Royer's
Consulting his lawyers,
Who fill forms in the chambers of Weyl.
[On Royer's talk]When Poussin outshone Hadamard
Was to fathom where no zeros are,
A domain which essentially
Goes back for a century,
But doesn't go back very far.
[On Ford's talk]
The methods that Kevin has found
Take off three or four all around;
Print the full calculation
For this presentation,
And his plane couldn't take off the ground.
[On Ford's talk]Bob Vaughan is the person most liable
For "smooth"; not a name very buyable.
We nominate humbly
The rendering "crumbly"
For Tenenbaum's beautiful "friable".
[On Tenenbaum's talk]
What Moree calls "psi-ex-wye-ology"
Is supporting a varied ecology,
Is the habitat viable ?
Says Tenenbaum, "friable".
So perhaps it's a branch of tribology.
[On Tenenbaum's talk]There's a song the americans know,
Though the Versing's inclined to be low:
In Tenenbaum's bible
Make everything friable.
"Well it ain't necessarily so."
[On Tenenbaum's talk]
Gerald Tenenbaum's book's so reliable,
Ev'ry recipe in it is tryable.
No pie in the sky,
There are more fish to fry,
And with Tenenbaum ev'rything's friable.
[On Tenenbaum's talk]Gerald Tenenbaum sprang a surprise,
A mind-blowing new name for psi-s.
Will they ruin my slumbers,
These friable numbers,
Or crumble to sand in my eyes ?
[On Tenenbaum's talk]
What a miracle Helgott can do,
With amplication there too.
When primes you can capture
The methods adapt to
Give silencing Moebius too.
[On Helfgott's talk]Lille doesn't have midsummer flowers.
When it rains, then it thunders for hours.
And the third of its features
Is giant mosquitos
That hang on the wall of the showers.
[On Lille's talk]
Primes one mod twelve don't grow so fast;
Non-residue classes rush past.
If deeper you delve,
Eleven mod twelve
Prefers to be first or the last.
[On Martin's talk]Greg Martin's astute observations,
How variance drives variations,
This family treasure
Is lost beyond measure
If the zeros have many relations.
[On Martin's talk]
What Turan and Knapowski could do
(Kaczorowski was into it too)
Got round the condition
Of general position
Which Sarnak would like to be true.
[On Martin's talk]In a jiffy the Pentium knows
What Diffie and Hellman propose,
If there's patternin its
Penultimate bits,
But no fits is what Friedlander shows.
[On Friedlander's talk]
Bob and Alice have got something nice.
"Keep it secret" would be our advice,
If their Emails are read
By the Deputy Head
Depends on Carmichael done twice.
[On Friedlander's talk]Whoever it's forwarded to,
It can only be opened by you.
Do you hope when you die,
They will all rush and try,
And believe that the message is true ?
[On Friedlander's talk]
Let's canonise Elliott's tricks,
Which span the first prime of Lin-nik's
His bible began
In its Genesis plan
With apocrypha to Chapter Six.
[On Elliott's talk]Approximate Moebius, losing
Large primes from a place of your choosing.
Bad characters crowd ?
Only one is allowed
If you trace every step that you're using.
[On Elliott's talk]
The Halasz machine in its coils
Runs only on natural oils,
But Elliott used
Artificial reduced,
With a sieve, or it clogs and it spoils.
[On Elliott's talk]The zeros of Epstein can slip
Past the one line, quite out of your grip.
Thus Akio's slide
Wasn't even too wide,
But went outside the critical strip.
[On Fujii's talk]
K suares and another K too
Times so you see something new,
Form Epstein on axis;
The mins and the maxes
What Bateman and Fujii would do.
[On Fujii's talk]The fractional part correlation
Should carry the whole information,
Were the zeros on-line
Set simply benign
By the power divine at Creation ?
[On Balazard's talk]
In Nyman's part-fractional space
We lack an orthogonal base
Inner products will come
Like a Dedekind sum
But both cots and Bernoulli embrace.
[On Balazard's talk]The greatest prime factor assign
To integers three in a line.
This function of n
Drops and rises again.
Does the difference ever change sign ?
[On Balog's talk]
Seven fourteen and seven fiftee
Use all primes up to seventeen
Add the factors of each,
Twenty nine you will reach
What on earth can it possibly mean ?
[On Balog's talk]Two consecutive integers call
Super-starnge if the factors are small,
And the sum of the primes
Is the same for both times.
Now do that with the bat in baseball !
[On Balog's talk]
A weight shaped like capital N
Will large on an interval when
The mean in a range
Has decided to change;
Distribution's less uniform then.
[On Coppola's talk]