Ravi Raghunathan
IIT Bombay
November 9, 2023
On the Primitivity and zeros of cuspidal automorphic $L$-functions: We will introduce an axiomatically defined set ${\mathfrak G}$ of Dirichlet series that is known to contain the $L$-functions of generic automorphic representations of $GL_n$ as well as other previously defined classes of Dirichlet series like the extended Selberg class. This set forms a monoid under multiplication. Weakening the hypotheses of the converse theorem of Weil, we will be able to establish that the $L$-functions of cuspidal automorphic representations of $GL_3$ are primitive in the monoid ${\mathfrak G}$ (these are the first examples of primitive series of degrees greater than $2$). Time permitting, we will discuss related questions on the zero sets of pairs of $L$-functions.
IIT Bombay
November 9, 2023
On the Primitivity and zeros of cuspidal automorphic $L$-functions: We will introduce an axiomatically defined set ${\mathfrak G}$ of Dirichlet series that is known to contain the $L$-functions of generic automorphic representations of $GL_n$ as well as other previously defined classes of Dirichlet series like the extended Selberg class. This set forms a monoid under multiplication. Weakening the hypotheses of the converse theorem of Weil, we will be able to establish that the $L$-functions of cuspidal automorphic representations of $GL_3$ are primitive in the monoid ${\mathfrak G}$ (these are the first examples of primitive series of degrees greater than $2$). Time permitting, we will discuss related questions on the zero sets of pairs of $L$-functions.