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Spring Semester 2012

Date / Time Speaker Title Location
9 March 2012
14:15-15:15 		Prof. Dr. Yves Martin
Universidad de Chile
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Number Theory Seminar

Title A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficients
Speaker, Affiliation Prof. Dr. Yves Martin, Universidad de Chile
Date, Time 9 March 2012, 14:15-15:15
Location 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.
A characterization of degree two Siegel cusp forms by the growth of their Fourier coefficientsread_more
HG G 43
23 March 2012
14:15-15:15 		Prof. Dr. Winfried Kohnen
Universität Heidelberg
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Number Theory Seminar

Title Conic theta functions
Speaker, Affiliation Prof. Dr. Winfried Kohnen, Universität Heidelberg
Date, Time 23 March 2012, 14:15-15:15
Location 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.
Conic theta functionsread_more
HG G 43
30 March 2012
14:30-15:30
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Number Theory Seminar

Title ETH Number Theory Days 2012
Speaker, Affiliation
Date, Time 30 March 2012, 14:30-15:30
Location HG
ETH Number Theory Days 2012
HG
31 March 2012
09:30-12:00
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Number Theory Seminar

Title ETH Number Theory Days 2012
Speaker, Affiliation
Date, Time 31 March 2012, 09:30-12:00
Location HG
ETH Number Theory Days 2012
HG
20 April 2012
14:15-15:15 		Dr. Paul Nelson
EPF Lausanne
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Number Theory Seminar

Title QUE on definite quaternion algebras
Speaker, Affiliation Dr. Paul Nelson, EPF Lausanne
Date, Time 20 April 2012, 14:15-15:15
Location 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.
QUE on definite quaternion algebrasread_more
HG G 43
27 April 2012
14:15-15:15 		Prof. Dr. Yuri Bilu
Université Bordeaux I
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Number Theory Seminar

Title Effective Diophantine analysis on modular curves
Speaker, Affiliation Prof. Dr. Yuri Bilu, Université Bordeaux I
Date, Time 27 April 2012, 14:15-15:15
Location 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.
Effective Diophantine analysis on modular curvesread_more
HG G 43
4 May 2012
14:15-15:15 		Dr. Ambrus Pal
Imperial College London
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Number Theory Seminar

Title The Brauer-Manin obstruction to the local-global principle for the embedding problem
Speaker, Affiliation Dr. Ambrus Pal, Imperial College London
Date, Time 4 May 2012, 14:15-15:15
Location 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.
The Brauer-Manin obstruction to the local-global principle for the embedding problemread_more
HG G 43
18 May 2012
14:15-15:15 		Dr. Peter Bruin
Universität Zürich
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Number Theory Seminar

Title Computing coefficients of modular forms
Speaker, Affiliation Dr. Peter Bruin, Universität Zürich
Date, Time 18 May 2012, 14:15-15:15
Location 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.
Computing coefficients of modular formsread_more
HG G 43
25 May 2012
14:15-15:15 		Dr. Guillaume Ricotta
ETH Zurich
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Number Theory Seminar

Title Bounding sup norms of automorphic forms
Speaker, Affiliation Dr. Guillaume Ricotta, ETH Zurich
Date, Time 25 May 2012, 14:15-15:15
Location 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.
Bounding sup norms of automorphic formsread_more
HG G 43
1 June 2012
14:15-15:15 		Prof. Dr. Gebhard Böckle
Universität Heidelberg
Details

Number Theory Seminar

Title The zero-distribution of Goss' Zeta-function for one non-rational function field
Speaker, Affiliation Prof. Dr. Gebhard Böckle, Universität Heidelberg
Date, Time 1 June 2012, 14:15-15:15
Location 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.
The zero-distribution of Goss' Zeta-function for one non-rational function fieldread_more
HG G 43

Organisers: Clemens Fuchs, Özlem Imamoglu, Emmanuel Kowalski, Richard Pink, Gisbert Wüstholz

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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