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Theorem

Voronoi Formula

Number Theory

A Voronoi Formula is an identity relating a sum built from the Fourier coefficients of an automorphic form to another such sum, with the terms on each side twisted by additive characters. It can be viewed as an analog of the Poisson summation formula adapted from ordinary abelian groups to the automorphic setting, and the version formulated for the group GL(2) is a standard tool in analytic number theory for studying automorphic forms and their L-functions. The name honors Georgy Voronoy.

Facts
Statement
A Voronoi formula is an identity relating a sum built from the Fourier coefficients of an automorphic form to another such sum, with the terms twisted by additive characters on each side. 1
Proof Year
1904 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Voronoi formula (Wikipedia)
  • Lead paragraph
    In mathematics, a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either side.
  • References, Voronoi 1904 entry
    Voronoi, G. (1904). Sur une fonction transcendente et ses applications a la sommation de quelques series. In Annales Scientifiques de l'Ecole Normale Superieure (Vol. 21, pp. 207-267).
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