• Corpus ID: 237091329

Modular forms, projective structures, and the four squares theorem

  title={Modular forms, projective structures, and the four squares theorem},
  author={Michael Eastwood and Ben Moore},
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… 

Three-generation solutions of equations of motion in heterotic supergravity

  • Maki TakeuchiTakanao TsuyukiHikaru Uchida
  • Mathematics
  • 2023
We study the generation number of massless fermions in compactifications recently found in heterotic supergravity. The internal spaces are products of two-dimensional spaces of constant curvatures,



A Quick Combinatorial Proof of Eisenstein Series Identities

The generating functions of the divisor sums σν(l) satisfy various identities. These are usually proved by making extensive use of the fact that they are modular forms. We give a short, completely

A First Course in Modular Forms

Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves

Conformal invariants and function-theoretic null-sets

The most useful conformal invar iants are obtained by solving conformMly invar ian t ex t remal problems. The i r usefulness derives f rom the fac t tha t they must automat ical ly satisfy a

Volume growth and puncture repair in conformal geometry

On certain arithmetical functions

  • Trans. Cambridge Philos. Soc. 22
  • 1916

On a non-linear partial differential equation satisfied by the logarithm of the Jacobian theta-functions, with arithmetical applications, Parts I and II

  • Indagationes Math
  • 1951