Let f be a Hecke eigenform of even integral weight on the full modular group, and let λ _sym^jf(n) denote the coefficients of the j-th symmetric power L-function attached to f. Extending recent results of Sharma and Sankaranarayanan (2022–2023), which treat the first and second power moments of these coefficients, we study the higher power moments corresponding to the third and fourth powers for j≥ 2. We obtain asymptotic estimates with refined error terms and establish generalizations over suitable arithmetic sets.
The classes of abelian groups that are (uniformly) strongly Hopfian abelian groups and, dually, (uniformly) strongly co-Hopfian abelian groups have been intensively studied by several authors, including Abdelalim–Chillali–Essanouni [1] and Abdelalim [2]. This paper extends these investigations in the case of (genuinely) mixed groups. For example, it is shown that a reduced group that is (uniformly) strongly co-Hopfian will always be (uniformly) strongly Hopfian. In addition, a result of Chekhlov–Danchev [4] characterizing when a torsion-free group is uniformly strongly Hopfian is generalized to the case of (global) Warfield groups.
Let f be an isometry of a median metric space. We show that if f attains its minimal displacement and no power of f has an inversion then f admits an axis. This generalizes to the median setting a result on isometries of CAT(0) cube complexes.
We develop a framework that enables us to study a broad class of special values of the Katz two-variable p-adic L-function, including certain special values lying outside the range of p-adic interpolation.
