178 citations · 1.1k across the 36 of their papers we have counts for
5 papers · 2 filters
A class of non-holomorphic modular forms III: real analytic cusp forms for
Francis Brown
We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass wav…
A class of non-holomorphic modular forms II : equivariant iterated Eisenstein integrals
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 con…
Algebraic de Rham theory for weakly holomorphic modular forms of level one
Francis Brown, Richard Hain
We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic d…
A class of non-holomorphic modular forms I
Francis Brown
This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the…
Integral points on curves, the unit equation, and motivic periods
Francis Brown
This paper recasts some of the recent literature on Kim's extension of Chabauty's method for bounding points on curves in the language of motivic periods. A variant of the higher A…