arXiv subjects

Sharon Anne Garthwaite

Publications and source records attributed to Sharon Anne Garthwaite.

2 recordsLinked to original sources

arXiv2013

Zeros of weakly holomorphic modular forms of levels 2 and 3

Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $Γ_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

math.NT↗

arXiv2013

Newton polygons for a variant of the Kloosterman family

We study the p-adic valuations of roots of L-functions associated with certain families of exponential sums of Laurent polynomials in n variables over a finite field. The families we consider are reflection and Kloosterman variants of diagonal polynomials. Using decomposition theorems of Wan, we determine the Newton and Hodge polygons of a non-degenerate Laurent polynomial in one of these families.

math.NT↗