论文标题
Mochizuki的推论的概率Szpiro，Baby Szpiro和显式Szpiro 3.12
Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12
论文作者
论文摘要
在\ cite {dupuy2020a}中，我们给出了Mochizuki不平等中的“不确定性” IND1，IND2，IND3的明确公式，以及最初的Theta数据的新介绍。在本文中，我们使用这些显式公式，以及\ cite [corallary 3.12] {iut3}的概率表述来得出Szpiro不平等的变体（本着\ cite {iut4}的精神）。特别是，对于初始theta数据中的椭圆曲线，我们显示了如何得出均匀的szpiro（具有显式数值常数）。我们得到的不平等将比\ cite [theorem 1.10] {iut4}弱弱，但是证据更透明，可修改和用户友好。所有这些不等式均源自\ cite [corallary 3.12] {iut3}的概率版本，该{iut3}基于随机测量集的概念在\ cite {dupuy2020a}中提出。
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 are more transparent, modifiable, and user friendly. All of these inequalities are derived from an probabilistic version of \cite[Corollary 3.12]{IUT3} formulated in \cite{Dupuy2020a} based on the notion of random measurable sets.
