Local Langlands correspondence for the twisted exterior and symmetric square ε-factors of GLn

We will prove the equality of the local arithmetic and analytic epsilon- and L-factors attached to the twisted symmetric square and exterior square representations of GL(n) over a non-Archimedean local field. The twisted local factors are new and can not be obtained directly from the non-twisted case established by J.W. Cogell F. Shahidi and T.-L. Tsai in 2017 unless the representation is twisted by the square of a character. We use GSpin groups to define the corresponding local analytic factors by Langlands-Shahidi method, and reduce the proof to the stability of local coefficients. The local coefficients can be written as the Mellin Transform of certain partial Bessel functions. Then we prove the stability of local coefficients by generalizing the asymptotic expansions of partial Bessel functions based on the ideas of Cogdell Shahidi and Tsai.