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math.NT2026
A Kohnen-Zagier Formula in Level 1
Clayton Williams
In 1985 Kohnen used the Shimura correspondence to prove a general formula relating the coefficients of half-integral weight modular forms of level transforming with respect…
math.NT2024
On the Pair Correlation of Zeros of -Functions for Non-CM Newforms in Shifted Ranges
Di Liu, Clayton Williams, Alexandru Zaharescu
We study the pair correlation between zeros of a shifted auxiliary -function attached to a non-CM newform, the scale of which is a fixed constant. We prove an unconditional as…
math.NT2024
Hecke Relations for Eta Multipliers and Congruences of Higher-Order Smallest Parts Functions
Clayton Williams
We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, yielding congruences for their coefficients modulo powers of primes. As an application we…