A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
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一类非全态模形式II：等变迭代艾森斯坦积分
DOI：
10.1017/fms.2020.24
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
F. Brown
中科院分区：
文献类型：
--
作者：
F. Brown
我们在上半平面上引入一个新的实解析模形式族。他们可以说是最简单的一类“混合”版本的模块形式的水平一和构造出的真实的和虚部的迭代积分的全纯爱森斯坦系列。它们形成了一个函数代数，满足许多类似于经典全纯模形式的性质。特别地，它们允许在$q、\overline{q}$和$\log中展开|Q|只涉及有理数和单值多zeta值。这类函数中的第一个非平凡函数是实解析艾森斯坦级数。
We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of holomorphic Eisenstein series. They form an algebra of functions satisfying many properties analogous to classical holomorphic modular forms. In particular, they admit expansions in $q,\overline{q}$ and $\log |q|$ involving only rational numbers and single-valued multiple zeta values. The first nontrivial functions in this class are real-analytic Eisenstein series.