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P-adic L-function of GL(2n) via method of p-adic representation. Gehrmann, Lennart


P -adic L-functions for cohomological cuspidal automorphic representations of GL(2n) were first constructed by Ash and Ginzburg in the case of trivial coefficients. We will discuss a new construction, which works for arbitrary coefficient systems. The construction relies on the representation theory of p-adic groups as well as properties of the cohomology of p-arithmetic groups. This is a generalization of Spiessâ work on the GL(2)-case.

Related references:
L. Gehrmann, On Shalika models and p-adic L-functions, Israel Journal of Mathematics 226 Issue 1, (June 2018), 237â 294

A. Ash and D. Ginzburg, P -adic L-functions for GL(2n), Inventiones mathematicae 116 (1994), 27â 73.

M. Spiess, On special zeros of p-adic L-functions of Hilbert modular forms, Inventiones mathe- maticae 196 (2014), 69â 138

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