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 Aug 14 awarded Enlightened Aug 14 awarded Nice Answer Mar 26 awarded Yearling Dec 9 awarded Caucus Nov 10 comment How to find certain quadratic curves over $\mathbb{Q}$ Thanks. It is likely that there are solutions other than the unit circle. It is possible to generate a family of such curves? Nov 10 asked How to find certain quadratic curves over $\mathbb{Q}$ Nov 6 comment Hasse's theorem on elliptic curves over finite fields I think multiplicity-one theorem forbids such a construction. Wiles proves that $\lambda_p+\bar{\lambda_p}$ comes from the coeffecient of some modular form of weight 2, and multiplicity-one theorem asserts that coefficients from two modular (eigen)forms satisfy $a_p^2=b_p^2$ for almost all prime $p$ if and only if $a(p)=b(p)\chi(p)$, where $\chi$ is some quadratic character. Your construct forces $\chi(p)=-1$ for almost all prime $p$, which is not possible. Nov 2 comment Identities related to hypergeometric functions I use Clausen's formula and linear transformation formula for the deduction, and things might go bad for the hypergeometric functions are multi-valued around its singularities. A numerical computation on Mathematica suggest that A is true for $0\sqrt{2}-1$. Nov 2 comment Identities related to hypergeometric functions Hmm. A and B cannot be simultaneously true for the same k. I am wondering whether a transformation formula exists. RHS has a singular point at $\sqrt{2}-1$, and I need such a formula for analytic continuation, and I hope this would help. Nov 2 revised Identities related to hypergeometric functions added 16 characters in body Nov 2 comment Identities related to hypergeometric functions Eh, $K^{\prime}$ does not represent the derivative of $K$ in elliptic integral theory. It is $K(\sqrt{1-k^2})$ Nov 2 asked Identities related to hypergeometric functions Oct 7 comment Some questions on the formation of the BSD conjecture Hmm. I have read a nice paper of Franz Lemmermeyer with the title "Conics: A poor man's elliptic curves", where such analog is discussed. But I am still wondering how Tate found the analog of regulator on the elliptic curves. I don't think numerical computations will help to establish the refined BSD conjecture. Oct 5 asked Some questions on the formation of the BSD conjecture Sep 8 comment Integral point on certain cubic surfaces and rational parametric solutions @guy-in-seoul: He discuss about heights in the last chapter in his book. Sep 8 comment Integral point on certain cubic surfaces and rational parametric solutions @guy-in-seoul: I did take a look at Manin's book on cubic forms, and the construction is just the one he introduces in the introduction. But I am not sure if he ever talks about something about integral points in his book. Sep 7 comment Integral point on certain cubic surfaces and rational parametric solutions @GerryMyerson: Hmm. The denominators in the constructions are polynomials of (at least) four variables, and I'm not sure what an obstruction will be to prevent these polynomials from taking small values. Sep 7 asked Integral point on certain cubic surfaces and rational parametric solutions Aug 20 accepted How to bound the following sum Aug 20 comment How to bound the following sum @Assaultous2: Terence Tao once wrote on moebius function in his blog, and he stated that $\{x/i\}$ has bounded variation, which is key to the proof of the identity $\sum\mu(n)/n=0$. The statement of Tao is the motivation of this question.