http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文 P2 Introduction
Theorem. 7We shall regard X as the “λ-line” - i.e., we shall regard the standard coordinate on X as the “λ” in the Legendre form “y2 = x(x-1)(x-λ)” of the Weierstrass equation defining an elliptic curve -
P34 Corollary 5.2. (Construction of suitable µ6-initial Θ-data) Write X for the projective line over Q; D ⊆ X for the divisor consisting of the three points “0”, “1”, and “∞”; (Mell)Q for the moduli stack of elliptic curves over Q. We shall regard X as the “λ-line” - i.e., we shall regard the standard coordinate on X as the “λ” in the Legendre form “y2 =x(x - 1)(x - λ)” of the Weierstrass equation defining an elliptic curve - 0302１３２人目の素数さん2021/02/27(土) 12:51:48.66ID:f+hU2HEr>>301 >the Legendre form >ここらが重要キーワードですね
The respective complete elliptic integrals are obtained by setting the amplitude, Φ, the upper limit of the integrals, to π/2.
The Legendre form of an elliptic curve is given by y2 = x(x-1)(x-λ)
Numerical evaluation The classic method of evaluation is by means of Landen's transformations. Descending Landen transformation decreases the modulus k k towards zero, while increasing the amplitude Φ. Conversely, ascending transformation increases the modulus towards unity, while decreasing the amplitude. In either limit of k, zero or one, the integral is readily evaluated.
Most modern authors recommend evaluation in terms of the Carlson symmetric forms, for which there exist efficient, robust and relatively simple algorithms. This approach has been adopted by Boost C++ Libraries, GNU Scientific Library and Numerical Recipes.[3] 0303１３２人目の素数さん2021/02/27(土) 13:31:25.71ID:+FXN4YNO>>301-302 阿多岡 貴様には無理 諦めろ 0304１３２人目の素数さん2021/02/27(土) 13:37:15.44ID:+FXN4YNO 阿多岡のニッポン自慢 キモイ 0305１３２人目の素数さん2021/02/27(土) 13:38:12.64ID:+FXN4YNO 人生の負け犬 阿多岡はガソリンかぶって焼身自殺な 🐖の丸焼きｗｗｗｗｗｗｗ 0306１３２人目の素数さん2021/02/27(土) 13:43:48.55ID:+FXN4YNO セカイ系 https://ja.wikipedia.org/wiki/%E3%82%BB%E3%82%AB%E3%82%A4%E7%B3%BB
銅 記事を真に受けてニッポン数学バンザイとわめく愛国馬鹿の阿多岡ｗ 0322１３２人目の素数さん2021/02/28(日) 07:44:47.62ID:ba03IeOv No State No Evil No Army No Murder No Money No Hunger 0323１３２人目の素数さん2021/02/28(日) 07:52:55.34ID:ba03IeOv 今年の目標 １．東京オリンピック開催阻止 ２．M子内親王の結婚の儀阻止
（参考） https://en.wikipedia.org/wiki/Modular_lambda_function Modular lambda function The relation to the j-invariant is[6][7] j(τ )= 256(1-λ (1-λ ))^3/{(λ (1-λ ))^2}= 256(1-λ +λ ^2)^3/{λ ^2(1-λ )^2} . which is the j-invariant of the elliptic curve of Legendre form y^2=x(x-1)(x-λ ) y^2=x(x-1)(x-λ )
https://www2.math.kyushu-u.ac.jp/~mkaneko/ https://www2.math.kyushu-u.ac.jp/~mkaneko/papers.html 金子昌信 論文 17. Supersingular j-invariants, hypergeometric series, and Atkin's orthogonal polynomials (with D. Zagier), AMS/IP Studies in Advanced Mathematics, vol. 7, 97--126, (1998). pdf https://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf SUPERSINGULAR j-INVARIANTS, HYPERGEOMETRIC SERIES, AND ATKIN’S ORTHOGONAL POLYNOMIALS M. Kaneko and D. Zagier §1. Introduction. The polynomial describing supersingularity in terms of the λ-invariant of E (defined by writing E over K¯ in Legendre form y 2 = x(x - 1)(x - λ)) has a well-known and simple explicit expression, but a convenient expression for the polynomial expressing the condition of supersingularity directly in terms of the j-invariant (i.e., in terms of a Weierstrass model over K, without numbering the 2-torsion points over K¯ ) is less easy to find. In this (partially expository) paper, we will describe several different ways of constructing canonical polynomials in Q[j] whose reductions modulo p give ssp(j). 0326１３２人目の素数さん2021/02/28(日) 09:34:19.70ID:ba03IeOv>>324 >あんたは complete idiot ◆OHIXyLapqcだよね
（>>5） http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文 p36 First, let us recall that if the once-punctured elliptic curve associated to EF fails to admit an F-core, (引用終り)
Analytic vs. algebraic This feature of Riemann surfaces allows one to study them with either the means of analytic or algebraic geometry. There is an equation
{\displaystyle [\wp '(z)]^{2}=4[\wp (z)]^{3}-g_{2}\wp (z)-g_{3},}{\displaystyle [\wp '(z)]^{2}=4[\wp (z)]^{3}-g_{2}\wp (z)-g_{3},} where the coefficients g2 and g3 depend on τ, thus giving an elliptic curve Eτ in the sense of algebraic geometry. Reversing this is accomplished by the j-invariant j(E), which can be used to determine τ and hence a torus.
Punctured spheres With three or more punctures, it is hyperbolic - compare pair of pants. 0333１３２人目の素数さん2021/02/28(日) 11:23:37.78ID:ba03IeOv>>331 正則行列も知らん落ちこぼれがいくらキーワードで検索しても 中身が読めないから無意味
