The rigid analytical regulator and K_2 of Drinfeld modular curves
Ambrus Pal
TL;DR
This paper computes a rigid analytical regulator on specific elements in the K_2 of Drinfeld modular curves, linking its value to special L-series values via the Rankin-Selberg method.
Contribution
It introduces an explicit evaluation of the rigid analytical regulator on K_2 elements of Drinfeld modular curves and connects it to L-series values.
Findings
Explicit regulator values are obtained for certain K_2 elements.
The regulator values are related to special values of L-series.
The method uses analogues of modular units and the Rankin-Selberg approach.
Abstract
We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K_2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of L-series using the Rankin-Selberg method.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds