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math.NT2025
Limit laws for cotangent and Diophantine sums
Bence Borda, Lorenz Frühwirth, Manuel Hauke
Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limi…
math.NT2024
A conjecture of Zagier and the value distribution of quantum modular forms
Christoph Aistleitner, Bence Borda
In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modul…