A note on a result of Bochner and Conrey-Ghosh about the Selberg class
It is well known [see \textit{S. Bochner}, Ann. Math. (2) 67, 29-41 (1958; Zbl 0082.29002) and \textit{J. B. Conrey} and \textit{A. Ghosh}, Duke Math. J. 72, 673-693 (1993; Zbl 0796.11037)], that there are no functions of degree \(0< d<1\) in the Selberg class of Dirichlet series with functional equation and Euler product. The author gives two simple proofs of this result. The first is based on the classical formula for the \(n\)-th coefficients of Dirichlet series; the second is based on Perron's formula. We remark that Molteni's first proof was already given by \textit{H.-E. Richert} [Acad. Serbe Sci., Publ. Inst. Mat. 11, 73-124 (1957; Zbl 0082.05802)], who apparently first proved the above result.
Dirichlet series with functional equation
scientific article; zbMATH DE number 1295494