Abstract
The aim of this article is to study the special values of Rankin triple product \(L\)-functions associated to Drinfeld type newforms of equal square-free levels. The functional equation of these \(L\)-functions is deduced from a Garrett-type integral representation and the functional equation of Eisenstein series on the group of similitudes of a symplectic vector space of dimension \(6\). When the associated root number is positive, we present a function field analogue of Gross–Kudla formula for the central critical value. This formula is then applied to the non-vanishing of \(L\)-functions coming from elliptic curves over function fields.
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Wei, FT. On Rankin triple product \(L\)-functions over function fields: central critical values. Math. Z. 276, 925–951 (2014). https://doi.org/10.1007/s00209-013-1227-9
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DOI: https://doi.org/10.1007/s00209-013-1227-9