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Zawartość zarchiwizowana w dniu 2024-06-12

Eichler cocycles and derivatives of l-functions of cusp forms


Research objectives and content
In my previous work, I have described a group-cocycle setting in which we can define what can be considered the generalization of the notion of modular integral and of the Eichler-Shimura isomorphism in relation to cocycle groups of higher dimension. Special values of derivatives of L-functions of weight k > 1 newforms can then be given an interpretation analogous to the one Manin has given for special values of the L-functions themselves. Motivated be this analogy, my first objective is to obtain information about the algebraic nature of the derivatives of the twisted L-functions evaluated at certain integers. Another objective is to use the algebraicity result I hope to obtain, together with certain techniques of Goldfeld to deduce facts related to Chowla's Conjecture.
Training content (objective, benefit and expected impact)
I expect that my stay in Max-Planck-Institut will be a very beneficial one, mainly because the above research program has been motivated, in large extent, by the work of mathematicians who belong to the faculty of that Institute (e.g. Manin, Zagier, etc.) and is based on their results. Furthermore it is important for the achievement of the above research goals to master the techniques these mathematicians use in their current research (especially the geometric ones).
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