American Institute of Mathematical Sciences

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

A note on L-series and Hodge spectrum of polynomials

Ricardo García López 1,

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].
Keywords: exponential sums, spectrum., limit Hodge structure, L-series.
Mathematics Subject Classification: 11L03, 14D0.
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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