Newton Polygons for a Variant of the Kloosterman Family
Women in Numbers 2: Research Directions in Number Theory, Contemporary Mathematics, Volume 606
We study the p-adic valuations of roots of L-functions associated with certain families of exponential sums of Laurent polynomials. The families we consider are reflection and Kloosterman variants of diagonal polynomials. Using decomposition theorems of Wan, we determine the Newton and Hodge polygons of a non-degenerate Laurent polynomial in one of these families.
Newton polygons for a variant of the Kloosterman family, Bellovin, R., Garthwaite, S., Ozman, E., Pries, R., Williams, C., Zhu, H., AMS/CRM Contemporary Mathematics Vol. 606: Women in Numbers 2: Research Directions in Number Theory, 2013, pp. 47--63.