# American Institute of Mathematical Sciences

2009, 16: 56-62. doi: 10.3934/era.2009.16.56

## A note on L-series and Hodge spectrum of polynomials

 1 Departament d'Algebra i Geometria. Universitat de Barcelona, Gran Via, 585. E-08007, Spain

Received  July 2009 Revised  September 2009 Published  December 2009

We compare on the one hand the combinatorial procedure described in [1] which gives a lower bound for the Newton polygon of the $L$-function attached to a commode, non-degenerate polynomial with coefficients in a finite field and on the other hand the procedure which gives the Hodge theoretical spectrum at infinity of a polynomial with complex coefficients and with the same Newton polyhedron. The outcome is that they are essentially the same, thus providing a Hodge theoretical interpretation of the Adolphson-Sperber lower bound which was conjectured in [1].
Citation: Ricardo García López. A note on L-series and Hodge spectrum of polynomials. Electronic Research Announcements, 2009, 16: 56-62. doi: 10.3934/era.2009.16.56
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