This article demonstrates a new proof of Jacquet’s local converse conjecture, using Rankin-Selberg convolutions in number theory.
Key Points
To construct integrals representing the product of Rankin-Selberg L-functions and establish their properties to prove Jacquet’s local converse conjecture.
Developed a family of integrals for Rankin-Selberg L-functions for GL_l × GL_m and GL_l × GL_n when m+n<l.
Reduced integrals when n=0 to classical Rankin-Selberg convolution integrals, extending existing work.
Defined local gamma factors based on these integrals.
The new integrals generalize the classical JPSS integrals, illustrating broader mathematical relations.
Establishment of key properties of these integrals aids in proving the local converse conjecture.
Proof provides fresh insights into the relationship between L-functions and local factors.