Hotel. June, 27 June, 29

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1 Hotel June, 27 June, 29 A reservation has been made for the non local speakers for two nights (check-in is June, 27 and check-out is June, 29). You should have nothing to pay (except maybe a small local tax). The hotel is the Inter-hotel Volcans. It is located 6, rue Sainte Rose in Clermont-Ferrand. To go there from the train station, you can walk for 20 minutes. You can also go there by bus (also 20 minutes, a single bus ticket is required): At bus station Gare SNCF, take the bus B in the direction of Stade Marcel Michelin. Leave the bus at the station Stade Marcel Michelin. Take trawmay A in the direction of La Pardieu Gare. Leave the tramway at the station Gaillard and walk for 3 minutes: Follow Avenue des États Unis (50 meters) Go on Place Gaillard (10 meters) Enter rue Sainte Rose.

2 Laboratoire de mathématiques Blaise Pascal To go to the Laboratoire de mathématiques Blaise Pascal from the hotel, you should take the tramway A at the station Gaillard in the direction of La Pardieu Gare. Leave the tramway at the station Campus. Then, to join the math building, cross the railway and walk perpendicular to the railway for a few minutes. After a few ascending steps, the math building is located on your left. We shall meet at the second floor.

3 On denominators of values of twisted L-functions Siegfried Bocherer Universität Mannheim June, 28 9:30 It is well known (generalized Clausen-von Staudt Theorems by Leopoldt and Carlitz) that generalized Bernoulli numbers tend to have less denominators than ordinary Bernoulli numbers. This can be rephrased as a statement concerning denominators of values of Dirichlet L-functions, viewed as twists of the Riemann zeta function. We discuss cases where we can get similar statements about the denominators of critical values of twists of more general L-functions, in particular for certain types of automorphic L-functions.

4 On the mod p kernel of the theta operator and Eisenstein series Sho Takemori Max-Planck-Institut für Mathematik June, 28 11:00 Prof. Boecherer and Prof. Nagaoka generalized Ramanujan s theta operator to Siegel modular form case. We are interested in investigating the mod p kernel of the theta operator. In this talk, we will construct some elements of the mod p kernel of the theta operator using Siegel-Eisenstein series of odd degrees. I will also talk about a similar result in hermitian modular form case. This is a joint work with Prof. Nagaoka. I also note that this work is heavily inspired by our discussion with Prof. Boecherer while his visiting at Kindai university.

5 Lunch June, Lunch will be served to the speakers at the university restaurant Les Hauts de l Artière. We shall go there together. This is at walking distance from our meeting room.

6 A multi-frey approach to some Fermat equations of signature (r,r,p) Nicolas Billerey Université Clermont-Auvergne June, 28 14:00 I will present a generalization of the modular method to some generalized Fermat equations of signature (r,r,p) where r is 5 or 13. The originality of the approach lies in the use of several Hellegouarch-Frey curves, some of which being defined over number fields. This is a joint work with Imin Chen, Luis Dieulefait and Nuno Freitas.

7 Rankin-Cohen deformations on Jacobi forms Emmanuel Royer Université Clermont-Auvergne June, 28 15:00 The sequence of Rankin-Cohen brackets is a formal deformation of the algebra of modular forms. In recent works with F. Dumas and with Y. Choie, F. Dumas and F. Martin, we construct formal deformations of the algebras of quasi modular forms and weak Jacobi forms. A first step in this description is a complete description of the Poisson structures on these algebras.

8 Admissible measures and Hermitian modular forms Alexei Pantchichkine Université Grenoble Alpes June, 28 16:30 For a prime p and a positive integer m, zeta function L F (s) is considered, attached to an Hermitian modular form F = H A(H)qH on the Hermitian upper half plane H m of degree m, where H runs through semi-integral positive definite Hermitian matrices of degree m, i.e. H Λ m (O) over the integers O of an imaginary quadratic field K, where q H = exp(2πitr(hz)). Analytic p-adic continuation of their zeta functions is constructed via p-adic measures, bounded or growing. Previously this problem was solved for the Siegel modular forms. Main result is stated in terms of the Hodge polygon P H (t) : [0, d] R and the Newton polygon P N (t) = P N,p (t) : [0, d] R of the zeta function L F (s) of degree d = 4m. Main theorem gives a p-adic analytic interpolation of the L values in the form of certain integrals with respect to Mazur-type measures. These p-adic measures are constructed from the Fourier coefficients of Hermitian modular forms, and from certain eigenvalues of Hecke operators on the unitary group. The integrality of such measures is proven in the ordinary case by Th.Bouganis in In the admissible case the difference h = P N (d/2) P H (d/2) is positive, a general result is shown on the existence of h-admissible (growing) measures of Amice-Vélu-type which produced an unbounded p-adic analytic interpolation of the L-values of growth log h p( ), using the Mellin transform of the constructed measures.

9 Dinner June, Dinner will be served to the speakers at the in-town restaurant La Gourmandine. We shall meet there at 8pm. The address of the restaurant is 8, rue des Minimes. The distance between the hotel and the restaurant is 300 meters.