2017/01/14 by Jerzy Kaczorowski, Kaczorowski, J., Alberto Perelli +1
Mathematics · #11F37 #11F66 #1M41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1701.03929
openalex publication_date 2017/01/14 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28
The standard twist F(s,α) of L-functions F(s) in the Selberg class has several interesting properties and plays a central role in the Selberg class theory. It is therefore natural to study its finer analytic properties, for example the functional equation. Here we deal with a special case, where F(s) satisfies a functional equation with the same Γ-factor of the L-functions associated with the cusp forms of half-integral weight; for simplicity we present our results directly for such L-functions. We show that the standard twist F(s,α) satisfies a functional equation reflecting s to 1-s, whose shape is not far from a Riemann-type functional equation of degree 2 and may be regarded as a degree 2 analog of the Hurwitz-Lerch functional equation. We also deduce some result on the growth on vertical strips and on the distribution of zeros of F(s,α).