Mean value theorems with smooth numbers
F. Majeed, Igor E. Shparlinski
TL;DR
This paper introduces new mean value theorems for exponential sums involving very smooth numbers, achieving power savings in regions where earlier bounds were ineffective.
Contribution
It provides novel mean value theorems for smooth numbers that improve bounds in previously inaccessible regions.
Findings
Achieved power savings over trivial bounds
Extended applicability of mean value theorems to smooth numbers
Enhanced understanding of exponential sums with smooth numbers
Abstract
We obtain new mean value theorems for exponential sums with very smooth numbers, which provide a power saving against the trivial bound in region where previous bounds do not apply.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Harmonic Analysis Research · Probability and Risk Models