On the Archimedean Euler factors for spin \(L\)-functions (Q1858610)

Andrianov associated the so-called spin \(L\)-function \(Z_f(s)\) to any Siegel modular form \(f\) of degree \(n\) and weight \(k\). Except for the cases \(u=1,2\) little is known about its analytic behaviour. In the paper under review the author obtains several formulas for the Archimedean Euler factor in any degree \(n\). He relates this factor to Andrianov's recursively defined factors and to symmetric power \(L\)-factors for GL\((2)\). Moreover the Archimedean \(\varepsilon\)-factor is computed. In the final section critical points of certain motives in the sense of Deligne are determined.