Geodesic
Values of certain $L$-series in positive characteristic
Federico Pellarin1
1 Université de Lyon, Lyon, France
Annals of mathematics, Tome 176 (2012) no. 3, pp. 2055-2093.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We introduce a class of deformations of the values of the Goss zeta function. We prove, with the use of the theory of deformations of vectorial modular forms as well as with other techniques, a formula for their value at $1$, and some arithmetic properties of values at other positive integers. Our formulas involve Anderson and Thakur’s function $\omega$. We discuss how our formulas may be used to investigate the existence of a kind of functional equation for the Goss zeta function.
DOI : 10.4007/annals.2012.176.3.13

Federico Pellarin 1

1 Université de Lyon, Lyon, France 
@article{10_4007_annals_2012_176_3_13,
     author = {Federico Pellarin},
     title = {Values of certain $L$-series  in positive characteristic},
     journal = {Annals of mathematics},
     pages = {2055--2093},
     publisher = {mathdoc},
     volume = {176},
     number = {3},
     year = {2012},
     doi = {10.4007/annals.2012.176.3.13},
     mrnumber = {2979866},
     zbl = {06121657},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.13/}
}
TY  - JOUR
AU  - Federico Pellarin
TI  - Values of certain $L$-series  in positive characteristic
JO  - Annals of mathematics
PY  - 2012
SP  - 2055
EP  - 2093
VL  - 176
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.13/
DO  - 10.4007/annals.2012.176.3.13
LA  - en
ID  - 10_4007_annals_2012_176_3_13
ER  - 
%0 Journal Article
%A Federico Pellarin
%T Values of certain $L$-series  in positive characteristic
%J Annals of mathematics
%D 2012
%P 2055-2093
%V 176
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.13/
%R 10.4007/annals.2012.176.3.13
%G en
%F 10_4007_annals_2012_176_3_13
Federico Pellarin. Values of certain $L$-series  in positive characteristic. Annals of mathematics, Tome 176 (2012) no. 3, pp. 2055-2093. doi : 10.4007/annals.2012.176.3.13. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.13/

Cité par Sources :