Modular Symbols and L-functions
نویسنده
چکیده
As the rst non-overview lecture in this seminar, we will be setting up a lot of notation, getting comfortable working with modular symbols, and then hopefully discussing some of the major inputs which make the theory work. The rst half of the talk we will work through the example of the unique cusp form of weight two and level 11 on X0(11). In the second half, we will bring in the theoretical results, which explain why modular symbols work. The two main results to pay attention to are Th'm 6.2 and Prop 7.6. We include a long discussion about cohomology for example, which won't be necessary in subsequent talks. The relevant material we intend to cover is in Section 1.1 of [BDInv] and Section 1.1 of [BDAnn]. We attempt to follow as closely as possible the notation used in these two papers. The proofs of the formulae can be found in [MTT] though the notation is di erent there. We made extensive use of Rob Pollack and Glenn Stevens' Notes from the AWS [PoSt] as well as unpublished notes of Bellaiche from a course taught at Brandeis [Bel]. We also used an unpublished manuscript of Brian Conrad's on Modular Forms and Galois representations [Con].
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تاریخ انتشار 2011