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A study in sums of products.
Étienne Fouvry1, Emmanuel Kowalski2, Philippe Michel3
1Université Paris Sud, Laboratoire de Mathématique, Campus d'Orsay, 91405 Orsay Cedex, France.
Summary
This study presents a generalized method for simplifying exponential sums. The findings offer practical applications in analytic number theory for trace functions.
Area of Science:
- Number Theory
- Algebraic Geometry
Background:
- Exponential sums are fundamental in analytic number theory.
- Trace functions play a crucial role in number theoretic functions.
- The Goursat-Kolchin-Ribet criterion provides a framework for studying independence conditions.
Purpose of the Study:
- To generalize cancellation techniques for exponential sums.
- To develop a method applicable to sums of products of trace functions.
- To facilitate applications within analytic number theory.
Main Methods:
- Developing a general version of cancellation in exponential sums.
- Utilizing trace functions that satisfy specific independence conditions.
- Leveraging the Goursat-Kolchin-Ribet criterion framework.
Main Results:
- A generalized cancellation method for exponential sums is established.
- The method applies to sums of products of trace functions.
- The results are presented in a readily applicable form for analytic number theory.
Conclusions:
- The generalized cancellation technique provides a powerful tool for analytic number theory.
- This work simplifies complex exponential sums involving trace functions.
- The applicability of the method enhances the study of number theoretic problems.
Keywords:
Riemann hypothesis over finite fieldsexponential sumsmonodromytrace functionsℓ-adic sheavesMore Related Videos
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