Central L-values up to squares

Abstract: This is a report on joint work -- in progress -- with A. Abdurrahman. Given an everywhere unramified symplectic Galois representation over a function field, we propose a conjectural formula for its central L-value up to squares in the coefficient field, in terms of a certain cohomological invariant of the representation. I'll describe three types of evidence for this conjecture, coming from numerical examples, topology, and automorphic forms. Then I will discuss (much more speculatively) what the ramified/number field analogue of the formula might be, and its potential relationship to a theory of "higher epsilon factors."

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html