Joerg Bruedern

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math.NT2024

Estimates for smooth Weyl sums on minor arcs

Joerg Bruedern, Trevor D. Wooley

We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of $α n^{k}$ . In particular, when $k \geq 6$ and…

math.NT2024

Partitio Numerorum: sums of squares and higher powers

Joerg Bruedern, Trevor D. Wooley

We survey the potential for progress in additive number theory arising from recent advances concerning major arc bounds associated with mean value estimates for smooth Weyl sums. W…

math.NT2021

Pairs of diagonal quartic forms: the non-singular Hasse principle

Joerg Bruedern, Trevor D. Wooley

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.