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A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma ( IF 1.389 ) Pub Date : 2020-05-28 , DOI: 10.1017/fms.2020.24
FRANCIS BROWN

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.

中文翻译:

一类非全态模形式II:等变迭代艾森斯坦积分

我们在上半平面上引入了一组新的实解析模形式。它们可以说是一级模形式的最简单的“混合”版本,由全纯 Eisenstein 级数的迭代积分的实部和虚部构成。它们形成满足许多类似于经典全纯模形式的性质的函数代数。特别是,他们承认在 $q,\overline{q}$ $\log |q|$ 只涉及有理数和单值多 zeta 值。此类中的第一个非平凡函数是实解析 Eisenstein 级数。
更新日期:2020-05-28
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