Generic Newton Slopes for Artin-Schreier-Witt Tower in two variables

Abstract

We prove that for any generic polynomial $f$ in two variables of degree $(d_1,d_2)$ over the rationals, for $p$ large enough the Newton slopes of the character power series $C_f^{\ast }({\chi }_m,s)$ of $f$ at $p$ is independent of the choice of the character ${\chi }_m$ (of conductor $p^m$); and the Newton slopes of the $L$-function $L_f^{\ast }({\chi }_m,s)$ of $f$ at $p$ is in weighted arithmetic progression.

18 pages

References in corpus (3)

• Asymptotic variation of L-functions of exponential sums
• Slopes of modular forms and the ghost conjecture (unabridged version)
• On the arithmetic of Z_p-extensions

Cited by in corpus (1)

• Generic Newton polygon for exponential sums in two variables with triangular base