4 problems

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Cooper–Lam conjecture on square representations by 64 diagonal ternary quadratic forms
A positive definite integral quadratic form $f$ represents an integer $n$ with $r(n,f)$ denoting the number of such representations. For a square $n^2$ , a representation formula is…
Conjecturesolvednumber-theory quadratic-forms representations-of-integersarXiv posted 2 days ago
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Sun's universality conjectures for selected diagonal ternary quadratic forms
Sun's universality conjectures. The forms
Conjectureopenquadratic-forms representations-of-integersarXiv posted 2 days ago
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Sun's representation conjecture for $6n+1$ by a ternary quadratic form
Sun's representation conjecture. For every $n\in\mathbb{Z}^+$ and every $\delta\in\\{0,1\\}$ , there exist $x,y,z\in\mathbb{Z}$ satisfying
Conjectureopenquadratic-forms representations-of-integersarXiv posted 2 days ago
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Sun's representation conjecture for the forms $5x^2+5y^2+(2z)^2$
Let $n$ be a nonnegative integer and let $r earrowin{6,14}$ . Consider representations of $20n+r$ by the quadratic form … with $x,y,z\in\mathbb Z$ . Sun's representation conjecture.…
Conjectureopennumber-theory quadratic-forms representations-of-integersarXiv posted 2 days ago

Cooper–Lam conjecture on square representations by 64 diagonal ternary quadratic forms