This is a survey of the structural invariants of the $L$-functions in the extended Selberg class $S^sharp$, covering some of their applications. In particular, we deal with the applications to the functional equation of the standard twist and to the classification of the functions in $S^sharp$ of degree $d=2$ and conductor $q=1$. Moreover, we give a new, purely algebraic, definition of the structural invariants and provide an explicit expression for them.
Structural invariants of L-functions and applications: a survey
A. Perelli
2022-01-01
Abstract
This is a survey of the structural invariants of the $L$-functions in the extended Selberg class $S^sharp$, covering some of their applications. In particular, we deal with the applications to the functional equation of the standard twist and to the classification of the functions in $S^sharp$ of degree $d=2$ and conductor $q=1$. Moreover, we give a new, purely algebraic, definition of the structural invariants and provide an explicit expression for them.
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