Math @ Duke

Publications [#338510] of Samit Dasgupta
Papers Published
 Dasgupta, S, Factorization of padic Rankin Lseries,
Inventiones Mathematicae, vol. 205 no. 1
(July, 2016),
pp. 221268, Springer Nature [doi]
(last updated on 2020/08/13)
Abstract: © 2015, SpringerVerlag Berlin Heidelberg. We prove that the padic Lseries of the tensor square of a pordinary modular form factors as the product of the symmetric square padic Lseries of the form and a Kubota–Leopoldt padic Lseries. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, who proved a factorization result for the Katz padic Lseries associated to the restriction of a Dirichlet character. Whereas Gross’s method is based on comparing circular units with elliptic units, our method is based on comparing these same circular units with a new family of units (called Beilinson–Flach units) that we construct. The Beilinson–Flach units are constructed using Bloch’s intersection theory of higher Chow groups applied to products of modular curves. We relate these units to special values of classical and padic Lfunctions using work of Beilinson (as generalized by Lei–Loeffler–Zerbes) in the archimedean case and Bertolini–Darmon–Rotger (as generalized by Kings–Loeffler–Zerbes) in the padic case. Central to our method are two compatibility theorems regarding Bloch’s intersection pairing and the classical and padic Beilinson regulators defined on higher Chow groups.


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