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Tunnell-type criteria for variants of the congruent number problem
We study the $θ$-congruent number problem for $\cosθ=\pm3/5$ and $\pm4/5$ using the generalized theta series construction of Sirolli--Tornaría. We describe its specialization to newforms of weight $2$ over $\mathbb Q$ with nontrivial square-free odd part of the level, and explain the reduction of qu
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