望月新一推论3.12的陈述：初始theta数据

Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12

In \cite{Dupuy2020a} we gave some explicit formulas for the "indeterminacies" Ind1,Ind2,Ind3 in Mochizuki's Inequality as well as a new presentation of initial theta data. In the present paper we use these explicit formulas, together with our probabilistic formulation of \cite[Corollary 3.12]{IUT3} to derive variants of Szpiro's inequality (in the spirit of \cite{IUT4}). In particular, for an elliptic curve in initial theta data we show how to derive uniform Szpiro (with explicit numerical constants). The inequalities we get will be strictly weaker than \cite[Theorem 1.10]{IUT4} but the proofs…

算术泰希米勒空间的构造 III：一块“罗塞塔石碑”与望月推论3.12的证明

Construction of Arithmetic Teichmuller Spaces III: A `Rosetta Stone' and a proof of Mochizuki's Corollary 3.12

本文作为算术泰希米勒空间系列研究的续作，证明了望月推论3.12，建立了可对照解读望月宇宙间泰希米勒理论与算术泰希米勒空间理论的“罗塞塔石碑”，还验证了望月理论中的粘合操作可由算术泰希米勒空间自然导出，并包含该推论的几何情形。

算术泰希米勒空间的构造 II：望月推论3.12的局部原型证明

Construction of Arithmetic Teichmuller spaces II: Proof of a local prototype of Mochizuki's Corollary 3.12

本文基于已确立的算术Teichmuller空间存在性，构造了望月$Θ_{gau}$-链接等对象，证明了赋值缩放性质与局部版望月推论3.12，还补充了相关链接与不确定性的内蕴证明。

Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers

We study the properties of Eisenstein-Kronecker numbers, which are related to special values of Hecke $L$-function of imaginary quadratic fields. We prove that the generating function of these numbers is a reduced (normalized or canonical in some literature) theta function associated to the Poincare bundle of an elliptic curve. We introduce general methods to study the algebraic and $p$-adic properties of reduced theta functions for CM abelian varieties. As a corollary, when the prime $p$ is ordinary, we give a new construction of the two-variable $p$-adic measure interpolating special values …

广义三重乘积p进L函数与椭圆曲线上的有理点

Generalized triple product $p$-adic $L$-functions and rational points on elliptic curves

本文推广并简化了三重乘积p进L函数的构造，将其与椭圆曲线上的Heegner点联系起来。