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
StatementA 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 Classification
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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.
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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