Critical points of the Eisenstein series E4 and application to the spectrum of the Lame operator

被引:0
作者
Chen, Zhijie [1 ]
Lin, Chang-Shou [2 ]
机构
[1] Tsinghua Univ, Dept Math Sci, Yau Math Sci Ctr, Beijing 100084, Peoples R China
[2] Natl Taiwan Univ, Ctr Adv Study Theoret Sci CASTS, 1 Sec 4,Roosevelt Rd, Taipei 10617, Taiwan
基金
国家重点研发计划;
关键词
Eisenstein series; Lame operator; MEAN-FIELD EQUATIONS; HYPERELLIPTIC CURVES; GREEN-FUNCTIONS; ZEROS;
D O I
10.4171/JST/501
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We give a complete description of the distribution of the critical points of the classical Eisenstein series E-4(tau). An application to the spectrum of the Lame operator is also given.
引用
收藏
页码:959 / 990
页数:32
相关论文
共 26 条
[1]  
Ahlfors L. V., 1953, International Series in Pure and Applied Mathematics
[2]  
AKHIEZER NI, 1990, ELEMENTS THEORY ELLI
[3]   On zeros of quasi-modular forms [J].
Balasubramanian, R. ;
Gun, Sanoli .
JOURNAL OF NUMBER THEORY, 2012, 132 (10) :2228-2241
[4]   On the spectrum of schrodinger operators with quasi-periodic algebro-geometric KdV potentials [J].
Batchenko, V ;
Gesztesy, F .
JOURNAL D ANALYSE MATHEMATIQUE, 2005, 95 (1) :333-387
[5]   Non-canonical extension of θ-functions and modular integrability of θ-constants [J].
Brezhnev, Yurii V. .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (04) :689-738
[6]   Mean field equations, hyperelliptic curves and modular forms: I [J].
Chai, Ching-Li ;
Lin, Chang-Shou ;
Wang, Chin-Lung .
CAMBRIDGE JOURNAL OF MATHEMATICS, 2015, 3 (1-2) :127-274
[7]   EXACT NUMBER AND NON-DEGENERACY OF CRITICAL POINTS OF MULTIPLE GREEN FUNCTIONS ON RECTANGULAR TORI [J].
Chen, Zhijie ;
Lin, Chang-Shou .
JOURNAL OF DIFFERENTIAL GEOMETRY, 2021, 118 (03) :457-485
[8]   Spectrum of the Lame operator and application, I: Deformation along Re τ=1/2 [J].
Chen, Zhijie ;
Fu, Erjuan ;
Lin, Chang-Shou .
ADVANCES IN MATHEMATICS, 2021, 383
[9]   Spectrum of the Lame Operator and Application, II: When an Endpoint is a Cusp [J].
Chen, Zhijie ;
Lin, Chang-Shou .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 378 (01) :335-368
[10]   CRITICAL POINTS OF THE CLASSICAL EISENSTEIN SERIES OF WEIGHT TWO [J].
Chen, Zhijie ;
Lin, Chang-Shou .
JOURNAL OF DIFFERENTIAL GEOMETRY, 2019, 113 (02) :189-226