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Lillian Beatrix Pierce

Anne Firor Scott Distinguished Professor of Mathematics
Mathematics
Duke Box 90320, Room 117 Physics Building, Durham, NC 27708
Duke Box 90320 120 Science Drive,, Durham, NC 27708

Scholarly Works - Preprints


Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization

Preprint · July 2, 2026 We develop the theory of strongly $n$-genuine polynomials $F(Y,X_1,\ldots,X_n)$, which have the property that the number of specializations $F(Y,X_1,\mathbf{x}')$ with $\mathbf{x}'=(x_2,\ldots,x_n) \in \mathbb{Z}^{n-1}$ (respectively $\mathbf{x}' \in \math ... Link to item Cite

A guide to Tauberian theorems for arithmetic applications

Preprint · April 22, 2025 A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, ranging from well-known ... Link to item Cite

A new type of superorthogonality

Preprint · December 17, 2022 Link to item Cite