College students’ reasons for leaving biomedical fields: Disenchantment with biomedicine or attraction to other fields?

Rosenzweig, Emily Q.; Harackiewicz, Judith M.; Hecht, Cameron A.; Priniski, Stacy J.; Canning, Elizabeth A.; Tibbetts, Yoi; Asher, Michael W.; Hyde, Janet S.

doi:10.1037/edu0000456

We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum 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 can be evaluated by a simple stationary phase estimate when k is not divisible by p, giving an essentially sharp bound for their size. We give a more complicated stationary phase estimate to evaluate them in the case when k is divisible by p. This gives both an upper bound and a lower bound showing the upper bound is essentially sharp. This generalizes previously known bounds in the case of ℤ/p. The lower bounds in the equal characteristic case have two applications to function field number theory, showing that certain short interval sums and certain moments of Dirichlet L-functions do not, as one might hope, admit square-root cancellation.

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