We investigate the vertical version of the Sato-Tate conjecture for some GL₂ automorphic representations over totally real fields with specified local components at a finite set of finite places.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-3, author = {Yuk-Kam Lau and Charles Li and Yingnan Wang}, title = {Quantitative analysis of the Satake parameters of GL2 representations with prescribed local representations}, journal = {Acta Arithmetica}, volume = {166}, year = {2014}, pages = {355-379}, zbl = {1317.11052}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-3} }
Yuk-Kam Lau; Charles Li; Yingnan Wang. Quantitative analysis of the Satake parameters of GL₂ representations with prescribed local representations. Acta Arithmetica, Tome 166 (2014) pp. 355-379. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-3/