Geodesic
Spherical Image of Local Hecke Series of Genus Four
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 676-680

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For the spherical image of a polynomial fraction, we obtain the explicit formula conjectured by Shimura in 1963 for generating Hecke series in the particular case of genus $4$. As in our previous work, we use formulas due to Andrianov for the Satake spherical map.
Keywords: Hecke operators, Dirichlet series, Euler factorization, spherical map. 
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     author = {K. A. Vankov},
     title = {Spherical {Image} of {Local} {Hecke} {Series} of {Genus} {Four}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {676--680},
     publisher = {mathdoc},
     volume = {81},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a3/}
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K. A. Vankov. Spherical Image of Local Hecke Series of Genus Four. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 676-680. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a3/