@article{12793, abstract = {Let F be a global function field with constant field Fq. Let G be a reductive group over Fq. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line P1Fq with two points of ramifications.}, author = {Yu, Hongjie}, issn = {1945-5844}, journal = {Pacific Journal of Mathematics}, keywords = {Arthur–Selberg trace formula, cuspidal automorphic representations, global function fields}, number = {1}, pages = {193--237}, publisher = {Mathematical Sciences Publishers}, title = {{ A coarse geometric expansion of a variant of Arthur's truncated traces and some applications}}, doi = {10.2140/pjm.2022.321.193}, volume = {321}, year = {2022}, }