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

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\sum_{n=1}^{\infty} (n^2+1)^{-s}$ for which such values have not been studied previously.
Classification : 11B68, 11M06, 30B50, 33E05 
@article{DOCMA_2008__13__a3,
     author = {Shimura, Goro},
     title = {The critical values of certain {Dirichlet} series},
     journal = {Documenta mathematica},
     pages = {775--794},
     publisher = {mathdoc},
     volume = {13},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a3/}
}
TY  - JOUR
AU  - Shimura, Goro
TI  - The critical values of certain Dirichlet series
JO  - Documenta mathematica
PY  - 2008
SP  - 775
EP  - 794
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a3/
LA  - en
ID  - DOCMA_2008__13__a3
ER  - 
%0 Journal Article
%A Shimura, Goro
%T The critical values of certain Dirichlet series
%J Documenta mathematica
%D 2008
%P 775-794
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a3/
%G en
%F DOCMA_2008__13__a3
Shimura, Goro. The critical values of certain Dirichlet series. Documenta mathematica, Tome 13 (2008), pp. 775-794. http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a3/