Geodesic
The critical values of certain Dirichlet series
Documenta mathematica, Tome 13 (2008), pp. 775-794

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We investigate the values of several types of Dirichlet series D(s) for certain integer values of s, and give explicit formulas for the value D(s) in many cases. The easiest types of D are Dirichlet L-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes ∑n=1∞​(n2+1)−s for which such values have not been studied previously.
DOI : 10.4171/dm/259
Classification : 11B68, 11M06, 30B50, 33E05 
Goro Shimura. The critical values of certain Dirichlet series. Documenta mathematica, Tome 13 (2008), pp. 775-794. doi: 10.4171/dm/259
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     author = {Goro Shimura},
     title = {The critical values of certain {Dirichlet} series},
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     volume = {13},
     doi = {10.4171/dm/259},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/259/}
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