On the L-series of F. Pellarin

Citations of this article
Mendeley users who have this article in their library.


The calculation, by L. Euler, of the values at positive even integers of the Riemann zeta function, in terms of powers of π and rational numbers, was a watershed event in the history of number theory and classical analysis. Since then many important analogs involving L-values and periods have been obtained. In analysis in finite characteristic, a version of Euler's result was given by L. Carlitz (1937) [Ca2], (1940) [Ca3] in the 1930s which involved the period of a rank 1 Drinfeld module (the Carlitz module) in place of π. In a very original work (Pellarin, 2011 [Pe2]), F. Pellarin has quite recently established a "deformation" of Carlitz's result involving certain L-series and the deformation of the Carlitz period given in Anderson and Thakur (1990) [AT1]. Pellarin works only with the values of this L-series at positive integral points. We show here how the techniques of Goss (1996) [Go1] also allow these new L-series to be analytically continued - with associated trivial zeroes - and interpolated at finite primes. © 2011 Elsevier Inc.




Goss, D. (2013). On the L-series of F. Pellarin. Journal of Number Theory, 133(3), 955–962. https://doi.org/10.1016/j.jnt.2011.12.001

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free