Naomi Sweeting

activity

20182022

collaborators

5 papers

math.NT2022

Tate classes and endoscopy for $GSp_{4}$ over totally real fields

Naomi Sweeting

The theory of endoscopy predicts the existence of large families of Tate classes on certain products of Shimura varieties, and it is natural to ask in what cases one can construct…

math.NT2020

Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory

Naomi Sweeting

Let $E / Q$ be an elliptic curve and let $K$ be an imaginary quadratic field. Under a certain Heegner hypothesis, Kolyvagin constructed cohomology classes for $E$ using $K$ -…

math.NT2018

On the zeros of a class of modular functions

Naomi Sweeting, Katharine Woo

We generalize a number of works on the zeros of certain level 1 modular forms to a class of weakly holomorphic modular functions whose $q$ -expansions satisfy \[ f_k(A, τ) \colon =…

math.NT2018

Formulas for Chebotarev densities of Galois extensions of number fields

Naomi Sweeting, Katharine Woo

We generalize the Chebotarev density formulas of Dawsey (2017) and Alladi (1977) to the setting of arbitrary finite Galois extensions of number fields $L / K$ . In particular, if $C \…

math.NT2018

Generating functions for power moments of elliptic curves over $F_{p}$

Katherine Gallagher, Lucia Li, Naomi Sweeting +2

Seminal works by Birch and Ihara gave formulas for the $m$ th power moments of the traces of Frobenius endomorphisms of elliptic curves over $F_{p}$ for primes $p \geq 5$ .…

Tate classes and endoscopy for GSp4​ over totally real fields

Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory

On the zeros of a class of modular functions

Formulas for Chebotarev densities of Galois extensions of number fields

Generating functions for power moments of elliptic curves over Fp​

Tate classes and endoscopy for $GSp_{4}$ over totally real fields

Generating functions for power moments of elliptic curves over $F_{p}$