Number Theory Seminars
Time: Friday at 14.15
Place: HWZ (HG G43)
Spring Semester 2012
| Date |
Speaker |
Title |
Time |
Location |
| 9-mar-2012 (fri) |
Yves Martin
|
A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficients
|
14:15-15:15 |
HG G 43 |
| Abstract: |
In this talk we will see that all cusp forms in the space of degree two Siegel modular forms are characterized by the growth of their Fourier coefficients. The corresponding statement in the case of elliptic modular forms is well-known and has an elementary proof, but such an argument does not admit a straightforward generalization to Siegel modular forms. In the talk I will show how to get the result in the Siegel case via a study of Jacobi cusp forms and the growth of their Fourier coefficients. |
| Speakers: |
Prof. Dr. Yves Martin
(Universidad de Chile)
Invited by: Ö. Imamoglu
|
|
| 23-mar-2012 (fri) |
Winfried Kohnen
|
Conic theta functions
|
14:15-15:15 |
HG G 43 |
| Abstract: |
We study a class of polyhedral functions called conic theta functions, which are closely related to classical theta functions. This is recent joint work with A. Folsom and S. Robins. |
| Speakers: |
Prof. Dr. Winfried Kohnen
(Universität Heidelberg)
Invited by: Ö. Imamoglu
|
|
| 30-mar-2012 (fri) |
|
ETH Number Theory Days 2012
|
|
HG |
|
|
| 31-mar-2012 (sat) |
|
ETH Number Theory Days 2012
|
|
HG |
|
|
| 6-apr-2012 (fri) |
|
Good Friday. No seminar.
|
|
HG G 43 |
|
|
| 20-apr-2012 (fri) |
Paul Nelson
|
QUE on definite quaternion algebras
|
14:15-15:15 |
HG G 43 |
| Abstract: |
We will describe a variant of the arithmetic quantum unique conjecture in the setting of functions on the finite set of ideal classes for an order of increasing level in a definite rational quaternion algebra. We present two proofs of this conjecture in the special case of forms of increasing prime square level; the second proof follows from recent joint work with A. Saha and A. Pitale. In the more difficult prime level case, we will discuss some ongoing work and conditional results. |
| Speakers: |
Dr. Paul Nelson
(EPF Lausanne)
Invited by: E. Kowalski, A. Saha
|
|
| 27-apr-2012 (fri) |
Yuri Bilu
|
Effective Diophantine analysis on modular curves
|
14:15-15:15 |
HG G 43 |
| Abstract: |
I will speak on two effective methods in Diophantine analysis: Baker's method and Runge's method, with a special emphasize to modular curves.
|
| Speakers: |
Prof. Dr. Yuri Bilu
(Université Bordeaux I)
|
|
| 4-may-2012 (fri) |
Ambrus Pal
|
The Brauer-Manin obstruction to the local-global principle for the embedding problem
|
14:15-15:15 |
HG G 43 |
| Abstract: |
We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the Brauer-Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel. In the course of our investigations we give a new, elegant description of the Tate duality pairing and prove a new theorem on the cup product in group cohomology. This is joint work with Tomer Schlank. |
| Speakers: |
Dr. Ambrus Pal
(Imperial College London)
Invited by: R. Pink
|
|
| 11-may-2012 (fri) |
|
TBA
|
|
HG G 43 |
|
|
| 18-may-2012 (fri) |
Peter Bruin
|
Computing coefficients of modular forms
|
14:15-15:15 |
HG G 43 |
| Abstract: |
We consider normalised Hecke eigenforms of weight k and level n. In recent years, Edixhoven, Couveignes et al. (for n = 1) and the speaker (generalisation to n ≥ 1) developed an algorithm that, given such an f and an integer m ≥ 1 in factored form, computes the m-th coefficient of the q-expansion of f in time polynomial in n, k and log m under the generalised Riemann hypothesis. I will describe this algorithm and explain some of the ingredients needed to prove its correctness. |
| Speakers: |
Dr. Peter Bruin
(Universität Zürich)
|
|
| 25-may-2012 (fri) |
Guillaume Ricotta
|
Bounding sup norms of automorphic forms
|
14:15-15:15 |
HG G 43 |
| Abstract: |
I will describe one possible way to bound the sup-norm of GL(n)-automorphic forms in several aspects including the spectral parameter and the level. |
| Speakers: |
Dr. Guillaume Ricotta
(ETH Zurich)
Invited by: E. Kowalski
|
|
| 1-jun-2012 (fri) |
Gebhard Böckle
|
The zero-distribution of Goss' Zeta-function for one non-rational function field
|
14:15-15:15 |
HG G 43 |
| Abstract: |
For certain integer rings A of global function fields, Goss defines a Zeta-function which to each p-adic integer n attaches, in a continuous way, an entire power series f_n over a complete non-archimedean field C_\infty of positive characteristic. Following the classical example of the Riemann zeta-function, he asks for the distribution of the zeroes of these functions. For A=F_q[t] work of Diaz-Vargas, Poonen and Sheats and Wan on the Newton polygons of the power series f_n yields that all roots of all f_n are simple and have pairwise distinct valuations.
In the talk we shall give a general introduction to the zeta-functions of Goss and recall the result for F_q[t]. Then we shall describe the Newton polygons of the f_n for A=F_2[x,y]/(y^2+y+x^3+x+1) explicitly. It follows that, with the exception of the two smallest roots (in absolute value), all roots of the f_n are simple and have pairwise distinct absolute values. For general A no conjecture seems known. In some cases, we present numerical evidence. If time permits we give some indication of the proofs. |
| Speakers: |
Prof. Dr. Gebhard Böckle
(Universität Heidelberg)
Invited by: R. Pink
|
|
The seminar is organized by G. Wüstholz, R. Pink, Ö. Imamoglu, E. Kowalski and C. Fuchs. If you have any questions send an email to one of the organizers.
