Ramesh Sreekantan
K_1 of products of Drinfeld modular curves and special values of L-functions.
Пт, 09/04/2009 - 12:10 — SomNambulAuthors: Ramesh Sreekantan
Subjects: Number Theory
AbstractBeilinson obtained a formula relating the special value of the L-function of
H^2 of a product of modular curves to the regulator of an element of a motivic
cohomology group - thus providing evidence for his general conjectures on
special values of L-functions. In this paper we prove a similar formula for the
L-function of the product of two Drinfeld modular curves providing evidence for
an analogous conjecture in the case of function fields.Higher order modular forms and mixed Hodge theory.
Пт, 09/04/2009 - 12:10 — SomNambulAuthors: Ramesh Sreekantan
Subjects: Number Theory
AbstractIn this paper we introduce a certain space of higher order modular forms of
weight 0 and show that it has a Hodge structure coming from the geometry of the
fundamental group of a modular curve. This generalizes the usual structure on
classical weight 2 forms coming from the cohomology of the modular curve.
Further we construct some higher order Poincare series to get higher order
higher weight forms and using them we define a space of higher weight, higher
order forms which has a mixed Hodge structure as well.
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