6 papers
Sums of Hecke eigenvalues along polynomial sequences and base change for
Katharine Woo
We study sums of absolute values of Hecke eigenvalues of representations that are tempered at all finite places. We show that these sums exhibit logarithmic saving…
Counting points in thin sets: A survey
Dante Bonolis, Lillian B. Pierce, Katharine Woo
In the 1980's Serre asked how many points of bounded height can lie in a thin set. This has motivated significant research ever since, culminating in a series of recent breakthroug…
Small scale distribution of linear patterns of primes
Mayank Pandey, Katharine Woo
Let be a system of linear forms with finite complexity. In their seminal paper, Green and Tao showed the following prime number theorem for values of the system : $$\sum_{x\…
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 -expansions satisfy \[ f_k(A, τ) \colon =…
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 . In particular, if $C \…
Generating functions for power moments of elliptic curves over
Katherine Gallagher, Lucia Li, Naomi Sweeting +2
Seminal works by Birch and Ihara gave formulas for the th power moments of the traces of Frobenius endomorphisms of elliptic curves over for primes .…