• Corpus ID: 237091329

Modular forms, projective structures, and the four squares theorem

@inproceedings{Eastwood2021ModularFP,
  title={Modular forms, projective structures, and the four squares theorem},
  author={Michael Eastwood and Ben Moore},
  year={2021}
}

• M. Eastwood, B. Moore
• Published 14 August 2021
• Mathematics

It is well-known that Lagrange’s four-square theorem, stating that every natural number may be written as the sum of four squares, may be proved using methods from the classical theory of modular forms and theta functions. We revisit this proof. In doing so, we concentrate on geometry and thereby avoid some of the tricky analysis that is often encountered. Guided by projective differential geometry we find a new route to Lagrange’s theorem. An artist’s impression of the action of Γ0(4) on the unit disc. In the Polish wycinanka lowicka style by Katarzyna Nurowska. 2010 Mathematics Subject Classification. 11F03, 11F27, 53A20. 1 ar X iv :2 10 8. 06 43 3v 1 [ m at h. N T ] 1 4 A ug 2 02 1 2 M. EASTWOOD AND B. MOORE