Simultaneous equidistribution of coupled periodic geodesics and CM points from rational planes in quadratic 4-space under Linnik splitting condition, using joining classification.
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A local-global principle holds for primitive representations of binary quadratic forms by quaternary quadratic forms.
Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.
Sums of absolute Hecke eigenvalues for GL(2) representations exhibit logarithmic savings over trivial bounds if and only if the representation is cuspidal, with a connection drawn to base change.
citing papers explorer
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Planes in quadratic 4-space and associated shapes of lattices
Simultaneous equidistribution of coupled periodic geodesics and CM points from rational planes in quadratic 4-space under Linnik splitting condition, using joining classification.
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Representations of binary quadratic forms by quaternary quadratic forms
A local-global principle holds for primitive representations of binary quadratic forms by quaternary quadratic forms.
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Counting points on a family of degree one del Pezzo surfaces
Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.
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Sums of Hecke eigenvalues along polynomial sequences and base change for $\text{GL}(2)$
Sums of absolute Hecke eigenvalues for GL(2) representations exhibit logarithmic savings over trivial bounds if and only if the representation is cuspidal, with a connection drawn to base change.