Patrick Sargos
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View article: A fourth derivative test for exponential sums
A fourth derivative test for exponential sums Open
We give an upper bound for the exponential $\sum_{m=1}^M \exp( 2iπf (m))$ in terms of $M$ and $λ$, where $λ$ is a small positive number which denotes the size of the fourth derivative of the real valued function $f$. The classical van der …
View article: A mean-value theorem for exponential sums. Applications to Weyl's inequality
A mean-value theorem for exponential sums. Applications to Weyl's inequality Open
We study the mean value of sixth power of some exponential sums following an idea due to Bombieri and Iwaniec. The result applies to Weyl's inequality, following an idea due to Heath-Brown