2 papers
math.NT2024
Sign changes along geodesics of modular forms
Dubi Kelmer, Alex Kontorovich, Christopher Lutsko
Given a compact segment, , of a cuspidal geodesic on the modular surface, we study the number of sign changes of cusp forms and Eisenstein series along . We prove uncondition…
math.SP2022
Sarnak's spectral gap question
Dubi Kelmer, Alex Kontorovich, Christopher Lutsko
We answer in the affirmative a question of Sarnak's from 2007, confirming that the Patterson-Sullivan base eigenfunction is the unique square-integrable eigenfunction of the hyperb…