A local-global principle holds for primitive representations of binary quadratic forms by quaternary quadratic forms.
The mixing conjecture under GRH
3 Pith papers cite this work. Polarity classification is still indexing.
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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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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.