3 papers
math.NT2025
Real part of cycle integrals and conjectures of Kaneko
Paloma Bengoechea, Sebastián Herrero, Ãzlem Imamoglu
We prove two of Kaneko's conjectures on the "values" of the modular function at real quadratic irrationalities: we prove the lower bound $\mathrm{Re}(\mathrm{…
math.NT2024
Twisted traces of modular functions on hyperbolic -space
Sebastián Herrero, Ãzlem Imamoglu, Anna-Maria von Pippich +1
We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic -space and show that they are essentially given by Fourier coefficients of the $j…
math.NT2024
Special values of Green's functions on hyperbolic -space
Sebastián Herrero, Ãzlem Imamoglu, Anna-Maria von Pippich +1
Gross, Kohnen and Zagier proved an averaged version of the algebraicity conjecture for special values of higher Green's functions on modular curves. In this work, we study an analo…