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Emmanuel Lecouturier一直致力于 研究代数数论领域,特别是与Eisenstein同余相关的问题。他的博士论文专门研究了Mazur's Eisenstein ideal,部分论文发表于[1]。他的论文引入了“Higher Eisenstein elements”的概念,这是Eisenstein ideal的一种“广义特征向量”。最近,他致力于Eisenstein ideal理论的算术应用,如L-函数的算术(与J. Wang教授合著[4])。他目前的主要研究兴趣在于A. Venkatesh教授关于“derived Hecke operators”的猜想。他研究了[3]中权重形式的案例,目前正在与L. Merel教授合作研究相关课题
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[1] Higher Eisenstein elements, higher Eichler formulas and ranks of Hecke algebras,
Inventiones mathematicae
, 223, pp. 485–595, 2021.
[2] On the Mazur–Tate conjecture for prime conductor and Mazur's Eisenstein ideal,
American Journal of Mathematics
, Volume 145, Number 5, pp. 1365-1387, 2023.
[3] On triple product L-functions and a conjecture of Harris–Venkatesh,
International Mathematics Research Notices
, Volume 2023, Issue 22, pp. 19476–19506, 2023.
[4] (With Jun Wang) On the arithmetic of special values of L-functions for certain abelian varieties with a rational isogeny, 2023, https://arxiv.org/abs/2305.00643