Christopher Lutsko

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math.NT2026

Lax-Phillips orbit counting in higher rank

Alex Kontorovich, Christopher Lutsko

Given a discrete lattice, $I^ < SL_{m} (R)$ , and a base point $o \in R^{m}$ , let $N_{I^} (T)$ denote the number of points in the orbit $o \cdot I^$ whose (E…

math.NT2025

Norm bounds on Eisenstein series

Dubi Kelmer, Alex Kontorovich, Christopher Lutsko

We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3…

math.NT2025

Sign changes along geodesics of modular forms

Dubi Kelmer, Alex Kontorovich, Christopher Lutsko

Given a compact segment, $I^^{2}$ , of a cuspidal geodesic on the modular surface, we study the number of sign changes of cusp forms and Eisenstein series along $I^^{2}$ . We prove unconditi…