Kummer's conjecture for cubic Gauss sums

DOI10.1007/s11856-000-1273-yzbMath0989.11042OpenAlexW615705420WikidataQ61051308 ScholiaQ61051308MaRDI QIDQ5932012

D. R. Heath-Brown

Publication date: 28 July 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:16c3966e-61cb-499d-839c-559b3794fcff

zbMATH Keywords

cubic Gauss sumsKummer conjecturemean-square estimate for Dirichlet seriessieve methodTauberian methodVaughan-Vinogradov method

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Gauss and Kloosterman sums; generalizations (11L05) Applications of sieve methods (11N36) Other analytic theory (11R47)

Related Items (17)

Low-lying zeros of cubic Dirichlet \(L\)-functions and the ratios conjecture ⋮ The mean values of cubic \(L\)-functions over function fields ⋮ On zeros of cubic \(L\)-functions ⋮ An improved spectral large sieve inequality for ${\rm SL}_3(\mathbb {Z})$ ⋮ On the distribution of modular square roots of primes ⋮ Mollified moments of cubic Dirichlet \(L\)-functions over the Eisenstein field ⋮ Mean square of quadratic Hecke character sum ⋮ LARGE VALUES OF FOR TH ORDER CHARACTERS AND APPLICATIONS TO CHARACTER SUMS ⋮ Mean values of some Hecke characters ⋮ On the negative Pell equation ⋮ A quadratic large sieve inequality over number fields ⋮ Mean values with cubic characters ⋮ Moments of quadratic Hecke \(L\)-functions of imaginary quadratic number fields ⋮ First moment of Hecke \(L\)-functions with quartic characters at the central point ⋮ One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke -functions ⋮ Value-distribution of cubic Hecke \(L\)-functions ⋮ The distribution of \(p\)-torsion in degree \(p\) cyclic fields

Cites Work

• A cubic analogue of the theta series.
• On the distribution of Kummer sums.
• Hilbert's Inequality
• A mean value estimate for real character sums
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