Newton slopes for Artin-Schreier-Witt towers

DOI10.1007/s00208-015-1262-4zbMath1348.11049arXiv1310.5311OpenAlexW2384423389MaRDI QIDQ261452

Liang Xiao, Daqing Wan, Christopher Davis

Publication date: 23 March 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5311

zbMATH Keywords

\(L\)-functionsArtin-Schreier-WittNewton slopes

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Curves over finite and local fields (11G20) Exponential sums (11T23) Congruences for modular and (p)-adic modular forms (11F33)

Related Items (16)

Slopes for higher rank Artin–Schreier–Witt towers ⋮ Slopes of eigencurves over boundary disks ⋮ IWASAWA THEORY FORp-TORSION CLASS GROUP SCHEMES IN CHARACTERISTICp ⋮ The stable property of Newton slopes for general Witt towers ⋮ Newton polygons of \(L\)-functions of polynomials \(x^d + a x^{d - 1}\) with \(p \equiv -1 \bmod d\) ⋮ Newton polygons of \(L\) functions of polynomials \(x^{d}+ax\) ⋮ A local analogue of the ghost conjecture of Bergdall-Pollack ⋮ Newton polygon of \(L\) function of \(x^d + \lambda x^{d -1} + \mu x \) ⋮ Exponential sums over finite fields ⋮ On \(L\)-functions of twisted \(T\)-adic exponential sums ⋮ On slopes of \(L\)-functions of \(\mathbb{Z}_p\)-covers over the projective line ⋮ Newton slopes for twisted Artin–Schreier–Witt towers ⋮ Class numbers and \(p\)-ranks in $\mathbb{Z}_p^d$-towers ⋮ \(T\)-adic exponential sums over affinoids ⋮ Genus growth in $\mathbb {Z}_p$-towers of function fields ⋮ Newton polygon of exponential sums in two variables with triangular base

Cites Work

• Unnamed Item
• \(T\)-adic exponential sums over finite fields
• Dimension variation of classical and \(p\)-adic modular forms
• The Riemann Hypothesis for the Goss zeta function for \(\mathbb{F}_q[T\)]
• On the \(p\)-adic Riemann hypothesis for the zeta function of divisors.
• A Riemann Hypothesis for characteristic \(p\) \(L\)-functions
• On the Riemann hypothesis for the characteristic \(p\) zeta function
• Dwork's conjecture on unit root zeta functions
• Slopes of eigencurves over boundary disks
• The \(L\)-functions of Witt coverings
• Variations of \(p\)-adic Newton polygons for \(L\)-functions of exponential sums
• The 2-adic eigencurve at the boundary of weight space

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