The first part gives the general theory of modular groups, modular forms and Hecke operators, with emphasis on the Hecke-Weil theory of the relation between modular forms and Dirichlet series. The second part is on the unit groups of quaternion algebras, which are seldom dealt with in books. The so-called Eichler-Selberg trace formula of Hecke operators follows next and the explicit computable formula is given. Skip to main content Skip to table of contents. Advertisement Hide. Modular Forms.
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Pages Automorphic Forms. L -Functions. Dokchitser will give a course on the BSD and his proof of the parity conjecture. Diamantis will give a course on higher order modular forms and their associated L-functions and Hecke theory.
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Doran will explore the various roles played by elliptic curves in the geometric aspects of string theory. His lectures will culminate in a description of recent work on growth rates of Gromov-Witten invariants and special values of L-functions.
Movasati will give a course explaining quasi-modular forms, connections with families of elliptic curves and fundamental differential equations for modular forms. The courses will be at the level of Masters courses, and while a background of basic Algebraic Number theory and Algebraic Geometry is helpful, it is not essential.
Arithmetic of Modular forms and Elliptic Curves
We propose to have 2- 3 lectures a day at the most, in order to leave ample time for informal discussions and a few research seminar level talks. Due to scheduling reasons the Workshop will start Tuesday, January 04th with check-in at am. Nikolaos Diamantis University of Nottingham Higher-order automorphic forms.
Tim Dokchitser Cambridge L-functions of elliptic curves. Amilcar Pacheco Universidade Federal do Rio de Janeiro Rational points on abelian varieties in pro-p towers of function fields.
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Talk 2 — — Oliver Lorscheild — Toroidal automorphic forms and the Riemann hypothesis. Talk 3 — — Matija Kazalicki — The Arithmetic of modular forms associated to Fermat curves.