AX-SCHANUEL FOR THE j-FUNCTION

被引：30

作者：

Pila, Jonathan ^{[1
]}

Tsimerman, Jacob ^{[2
]}

机构：

[1] Univ Oxford, Math Inst, Oxford, England

[2] Univ Toronto, Dept Math, Toronto, ON, Canada

来源：

DUKE MATHEMATICAL JOURNAL | 2016年 / 165卷 / 13期

基金：

加拿大自然科学与工程研究理事会; 英国工程与自然科学研究理事会;

关键词：

TRANSCENDENCE; FAMILIES; POINTS; FIELD;

D O I：

10.1215/00127094-3620005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove a functional transcendence statement for the j-function which is an analogue of the Ax-Schanuel theorem for the exponential function. It asserts, roughly, that atypical algebraic relations among functions and their compositions with the j-function are governed by modular relations.

引用

页码：2587 / 2605

页数：19

共 32 条

[21] O-minimality and the Andre-Oort conjecture for Cn
Pila, Jonathan
[J]. ANNALS OF MATHEMATICS, 2011, 173 (03) : 1779 - 1840
[22] Pink R, 2005, PROG MATH, V235, P251
[23] Pink R., 2005, PREPRINT
[24] kappa-Volume in R(n) and the generalized Pythagorean theorem
Porter, GJ
[J]. AMERICAN MATHEMATICAL MONTHLY, 1996, 103 (03) : 252 - 256
[25] ABSTRACT DIFFERENTIAL ALGEBRA AND ANALYTIC CASE .2.
SEIDENBERG, A
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 23 (03) : 689 - +
[26] SEIDENBERG A, 1958, P AM MATH SOC, V9, P159, DOI [DOI 10.1090/S0002-9939-1958-0093655-0, 10.1090/S0002-9939-1958-0093655-0]
[27] Tsimerman J., 2015, LONDON MATH SOC LECT, V421, P216
[28] Van Den Dries L., 1998, LONDON MATH SOC LECT, DOI 10.1017/CBO9780511525919
[29] THE ELEMENTARY THEORY OF RESTRICTED ANALYTIC FIELDS WITH EXPONENTIATION
VANDENDRIES, L
MACINTYRE, A
MARKER, D
[J]. ANNALS OF MATHEMATICS, 1994, 140 (01) : 183 - 205
[30] ON THE REAL EXPONENTIAL FIELD WITH RESTRICTED ANALYTIC-FUNCTIONS
VANDENDRIES, L
MILLER, C
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1994, 85 (1-3) : 19 - 56

← 1 2 3 4 →