arXiv subjects

Edna Jones

Publications and source records attributed to Edna Jones.

3 recordsLinked to original sources

arXiv2024

The Kloosterman circle method and weighted representation numbers of quadratic forms

We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of nonsingular integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, Sali\'{e} sums, and a principle of nonstationary phase. We briefly discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings.

math.NT↗

arXiv2023

Moments of Artin-Schreier L-functions

We compute moments of $L$-functions associated to the polynomial family of Artin--Schreier covers over $\mathbb{F}_q$, where $q$ is a power of a prime $p>2$, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $k^{\text{th}}$ moment for a large range of values of $k$, depending on the sizes of $p$ and $q$. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family.

math.NT↗

arXiv2020

Local Densities of Diagonal Integral Ternary Quadratic Forms at Odd Primes

We give formulas for local densities of diagonal integral ternary quadratic forms at odd primes. Exponential sums and quadratic Gauss sums are used to obtain these formulas. These formulas (along with 2-adic densities and Siegel's mass formula) can be used to compute the representation numbers of certain ternary quadratic forms.

math.NT↗