Exponential Sums
Weyl, Vinogradov, and bounds via Bombieri–Iwaniec.
Exponential Sums. Weyl, Vinogradov, and bounds via Bombieri–Iwaniec.
Foundations and canonical references
The standard treatments of exponential sums approach the subject from complementary angles. Davenport, Analytic Methods for Diophantine Equations and Diophantine Inequalities (2005) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for exponential sums include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2005Analytic Methods for Diophantine Equations and Diophantine Inequalitiesdavenport-2005
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