Math @ Duke

Publications [#338517] of Samit Dasgupta
Papers Published
 Dasgupta, S; Miller, A, A Shintanitype formula for GrossStark units over function fields,
Journal of Mathematical Sciences, vol. 16 no. 3
(December, 2009),
pp. 415440
(last updated on 2020/08/13)
Abstract: Let F be a totally real number field of degree n, and let H be a finite abelian extension of F. Let p denote a prime ideal of F that splits completely in H. Following Brumer and Stark, Tate conjectured the existence of a punit u in H whose padic absolute values are related in a precise way to the partial zetafunctions of the extension H/F. Gross later refined this conjecture by proposing a formula for the padic norm of the element u. Recently, using methods of Shintani, the first author refined the conjecture further by proposing an exact formula for u in the padic completion of H. In this article we state and prove a function field analogue of this Shintanitype formula. The role of the totally real field F is played by the function field of a curve over a finite field in which n places have been removed. These places represent the "real places" of F. Our method of proof follows that of Hayes, who proved Gross's conjecture for function fields using the theory of Drinfeld modules and their associated exponential functions.


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