An upper bound for Weil exponential sums over Galois rings and applications

1995 ◽  
Vol 41 (2) ◽  
pp. 456-468 ◽  
Author(s):  
P.V. Kumar ◽  
T. Helleseth ◽  
A.R. Calderbank
Keyword(s):  
Upper Bound ◽  
Exponential Sums ◽  
Galois Rings

scholarly journals An Upper Bound for the Extended Kloosterman Sums over Galois Rings

1998 ◽  
Vol 4 (3) ◽  
pp. 218-238 ◽  
Author(s):  
Abhijit G. Shanbhag ◽  
P. Vijay Kumar ◽  
Tor Helleseth
Keyword(s):  
Upper Bound ◽  
Kloosterman Sums ◽  
Galois Rings

scholarly journals On the fourth derivative test for exponential sums

2016 ◽  
Vol 28 (2) ◽  
Author(s):  
Olivier Robert
Keyword(s):  
Upper Bound ◽  
Exponential Sums ◽  
Exponential Sum ◽  
Fourth Derivative ◽  
Derivative Test

AbstractWe give an upper bound for the exponential sum ∑

ON THE ERROR TERM IN THE APPROXIMATE FUNCTIONAL EQUATION FOR EXPONENTIAL SUMS RELATED TO CUSP FORMS

2008 ◽  
Vol 04 (05) ◽  
pp. 747-756 ◽  
Author(s):  
ANNE-MARIA ERNVALL-HYTÖNEN
Keyword(s):  
Functional Equation ◽  
Upper Bound ◽  
Error Term ◽  
Exponential Sums ◽  
Cusp Forms ◽  
Approximate Functional Equation ◽  
Holomorphic Cusp Forms

We give a proof for the approximate functional equation for exponential sums related to holomorphic cusp forms and derive an upper bound for the error term.

scholarly journals A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Jianghua Li ◽  
Tingting Wang
Keyword(s):  
Asymptotic Formula ◽  
Upper Bound ◽  
Exponential Sums ◽  
Mean Value ◽  
Gauss Sums ◽  
Dedekind Sums ◽  
Analytic Method ◽  
Hybrid Mean Value ◽  
Classical Work ◽  
Upper Bound Estimate

The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.

scholarly journals IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES

2019 ◽  
Vol 7 ◽  
Author(s):  
RAF CLUCKERS ◽  
MIRCEA MUSTAŢĂ ◽  
KIEN HUU NGUYEN
Keyword(s):  
Upper Bound ◽  
Exponential Sums ◽  
Log Canonical Threshold ◽  
Log Canonical ◽  
Optimal Estimates

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of the estimates. We show that this covers optimally all situations of the conjectures for nonrational singularities by comparing the log canonical threshold with a local notion of the motivic oscillation index.

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