Abstract
The Ichino–Ikeda conjecture, and its generalization to unitary groups by N. Harris, gives explicit formulas for central critical values of a large class of Rankin–Selberg tensor products. The latter conjecture has been proved in full generality and applies to -values of the form , where and are cohomological automorphic representations of unitary groups and , respectively. Here and are hermitian spaces over a CM field, of dimension , of codimension 1 in , and denotes the twisted base change to .
This paper contains the first steps toward constructing a -adic interpolation of the normalized square roots of these -values, generalizing the construction in my paper with Tilouine on triple product -functions. It will be assumed that the CM field is imaginary quadratic, is a holomorphic representation and varies in an ordinary Hida family (of antiholomorphic forms). The construction of the measure attached to uses recent work of Eischen, Fintzen, Mantovan, and Varma.
Citation
Michael Harris. "Square root -adic -functions I: Construction of a one-variable measure." Tunisian J. Math. 3 (4) 657 - 688, 2021. https://doi.org/10.2140/tunis.2021.3.657
Information