American Institute of Mathematical Sciences

Advanced
  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
[1]

Gennady Bachman. Exponential sums with multiplicative coefficients. Electronic Research Announcements, 1999, 5: 128-135.

[2]

Emmanuel Schenck. Exponential gaps in the length spectrum. Journal of Modern Dynamics, 2020, 16: 207-223. doi: 10.3934/jmd.2020007
[3]

Geir Bogfjellmo. Algebraic structure of aromatic B-series. Journal of Computational Dynamics, 2019, 6 (2) : 199-222. doi: 10.3934/jcd.2019010
[4]

Assane Lo, Nasser-eddine Tatar. Exponential stabilization of a structure with interfacial slip. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6285-6306. doi: 10.3934/dcds.2016073
[5]

Damiano Foschi. Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals. Communications on Pure & Applied Analysis, 2005, 4 (3) : 569-588. doi: 10.3934/cpaa.2005.4.569
[6]

Sergei A. Nazarov, Rafael Orive-Illera, María-Eugenia Pérez-Martínez. Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations. Networks & Heterogeneous Media, 2019, 14 (4) : 733-757. doi: 10.3934/nhm.2019029
[7]

Yanqiong Lu, Ruyun Ma. Disconjugacy conditions and spectrum structure of clamped beam equations with two parameters. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3283-3302. doi: 10.3934/cpaa.2020145
[8]

Günter Leugering, Sergei A. Nazarov, Jari Taskinen. The band-gap structure of the spectrum in a periodic medium of masonry type. Networks & Heterogeneous Media, 2020, 15 (4) : 555-580. doi: 10.3934/nhm.2020014
[9]

Fabien Durand, Alejandro Maass. A note on limit laws for minimal Cantor systems with infinite periodic spectrum. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 745-750. doi: 10.3934/dcds.2003.9.745
[10]

Jonathan Meddaugh, Brian E. Raines. The structure of limit sets for $\mathbb{Z}^d$ actions. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4765-4780. doi: 10.3934/dcds.2014.34.4765
[11]

Hai-Liang Li, Hongjun Yu, Mingying Zhong. Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system. Kinetic & Related Models, 2017, 10 (4) : 1089-1125. doi: 10.3934/krm.2017043
[12]

Soohyun Bae, Yūki Naito. Separation structure of radial solutions for semilinear elliptic equations with exponential nonlinearity. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4537-4554. doi: 10.3934/dcds.2018198
[13]

Xu Xu, Xin Zhao. Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model. Discrete & Continuous Dynamical Systems, 2020, 40 (8) : 4777-4800. doi: 10.3934/dcds.2020201
[14]

James Benn. Fredholm properties of the $L^{2}$ exponential map on the symplectomorphism group. Journal of Geometric Mechanics, 2016, 8 (1) : 1-12. doi: 10.3934/jgm.2016.8.1
[15]

Irena Lasiecka, Roberto Triggiani. Heat--structure interaction with viscoelastic damping: Analyticity with sharp analytic sector, exponential decay, fractional powers. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1515-1543. doi: 10.3934/cpaa.2016001
[16]

Jae Gil Choi, David Skoug. Algebraic structure of the $ L_2 $ analytic Fourier–Feynman transform associated with Gaussian paths on Wiener space. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3829-3842. doi: 10.3934/cpaa.2020169
[17]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195
[18]

Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero. Chain recurrence and structure of $ \omega $-limit sets of multivalued semiflows. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2197-2217. doi: 10.3934/cpaa.2020096
[19]

Magdalena Foryś-Krawiec, Jana Hantáková, Piotr Oprocha. On the structure of $ \alpha $-limit sets of backward trajectories for graph maps. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021159
[20]

Xu Chen, Jianping Wan. Integro-differential equations for foreign currency option prices in exponential Lévy models. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 529-537. doi: 10.3934/dcdsb.2007.8.529

2020 Impact Factor: 0.929

Tools

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy