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math.NT2026

Murmurations in the depth aspect

Claire Burrin, Vivian Kuperberg, Min Lee +2

We compute the murmuration density function for the family of Hecke forms of weight $k$ and prime power level $N = ℓ^{a}$ , with $ℓ$ a fixed odd prime and $a \to \infty$ .

math.NT2024

Kloosterman sums on orthogonal groups

Catinca Mujdei

We study Kloosterman sums on the orthogonal groups $S O_{3, 3}$ and $S O_{4, 2}$ , associated to short elements of their respective Weyl groups. An explicit description for these sums i…