3 papers
math.NT2026
A note on the invariants of the -functions
Jerzy Kaczorowski, Alberto Perelli
We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an -functi…
math.NT2026
Multiple standard twists of -functions
Jerzy Kaczorowski, Alberto Perelli
The standard twist of -functions plays a fundamental role in the Selberg class theory. It is defined as an absolutely convergent Dirichlet series and admits meromorphic continua…
math.NT2025
-functions of degree and conductor : underlying ideas and a generalisation
Jerzy Kaczorowski, Alberto Perelli
We present a streamlined account of a recent theorem on the classification of the -functions of degree 2 and conductor 1 from the extended Selberg class. We also present a more…