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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2 Pith papers cite this work. Polarity classification is still indexing.
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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.
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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.