A stationary phase formula for exponential sums over $ℤ/p^{m}ℤ$ and applications to GL(3)-Kloosterman sums

DOI10.4064/aa-80-1-1-48zbMath0893.11032OpenAlexW965515422MaRDI QIDQ4345820

Publication date: 29 July 1997

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa-80-1-1-48

zbMATH Keywords

exponential sums Kloosterman sums $n$-dimensional version of Hensel's lemma $p$-adic stationary phase Fourier coefficients of $GL(3)$ Poincaré series Hessians of arbitrary valuation Kloosterman sets

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05) Fourier coefficients of automorphic forms (11F30) Varieties over finite and local fields (11G25)

Related Items (23)

Cyclotomic fields are generated by cyclotomic Hecke $L$-values of totally real fields ⋮ On the mean value of the two-term exponential sums with Dirichlet characters ⋮ Parametrization of Kloosterman sets and $\mathrm{SL}_3$-Kloosterman sums ⋮ The arithmetic Kuznetsov formula on $\mathrm{GL}(3)$. II: The general case ⋮ A four-variable automorphic kernel function ⋮ Applications of the Kuznetsov formula on $\mathrm{GL}(3)$. II: The level aspect ⋮ A study on functional independence of the Iwasawa power series ⋮ Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$ ⋮ Bessel functions and Kloosterman integrals on $\mathrm{GL}(n)$ ⋮ Matrix Kloosterman sums modulo prime powers ⋮ On sums of $\mathrm{SL}(3,\mathbb{Z})$ Kloosterman sums ⋮ On an exponential sum ⋮ Upper bounds on $n$-dimensional Kloosterman sums ⋮ Unnamed Item ⋮ Multiparametric exponential sums associated with quasi-homogeneous polynomial mappings ⋮ Global decomposition of $\operatorname{GL}(3)$ Kloosterman sums and the spectral large sieve ⋮ The arithmetic Kuznetsov formula on $\mathrm{GL}(3)$. I: The Whittaker case ⋮ Kloosterman sets in reductive groups ⋮ Mean value of some exponential sums and applications to Kloosterman sums ⋮ Symplectic Kloosterman sums and Poincaré series ⋮ An orthogonality relation for (with an appendix by Bingrong Huang) ⋮ On the size of 𝑝-adic Whittaker functions ⋮ The stationary-phase method for exponential sums with multiplicative characters.

This page was built for publication: A stationary phase formula for exponential sums over $ℤ/p^{m}ℤ$ and applications to GL(3)-Kloosterman sums