English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study p-adic hyper-Kloosterman sums, a generalization of the Kloostermansum with a parameter k that recovers the classical Kloosterman sum when k=2,over general p-adic rings and even equal characteristic local rings. These canbe evaluated by a simple stationary phase estimate when k is not divisible byp, giving an essentially sharp bound for their size. We give a more complicatedstationary phase estimate to evaluate them in the case when k is divisible byp. This gives both an upper bound and a lower bound showing the upper bound isessentially sharp. This generalizes previously known bounds of Cochrane, Liu,and Zhen in the case of $\mathbb Z_p$. The lower bounds in the equalcharacteristic case have two applications to function field number theory,showing that certain short interval sums and certain moments of DirichletL-functions do not, as one might hope, admit square-root cancellation.

The size of wild Kloosterman sums in number fields and function fields