Dubi Kelmer

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math.NT2025

The density Hypothesis for irreducible lattices in $PSL_{2} (R)^{d}$

Dubi Kelmer

We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $PSL_{2} (R)^{d}$ , extending previous results on the spherical density hy…

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…

math.NT2024

Effective density of values of indefinite ternary inhomogeneous quadratic forms

Dubi Kelmer

Given an inhomogeneous quadratic form $Q_{I^} ¾ (v) = Q (v + I^¾)$ with $Q$ an indefinite $Q$ -isotropic rational ternary form and $I^¾ \in R^{3}$ irrational, we prove an effecti…

The density Hypothesis for irreducible lattices in PSL2​(R)d

Norm bounds on Eisenstein series

Sign changes along geodesics of modular forms

Effective density of values of indefinite ternary inhomogeneous quadratic forms

The density Hypothesis for irreducible lattices in $PSL_{2} (R)^{d}$