In mathematics, Waldspurger's theorem, introduced by Jean-Loup Waldspurger (1981), is a result that identifies Fourier coefficients of modular forms of half-integral weight k+1/2 with the value of an L-series at s=k/2.
References Waldspurger, Jean-Loup (1981), "Sur les coefficients de Fourier des formes modulaires de poids demi-entier", Journal de Mathématiques Pures et Appliquées, Neuvième Série, 60 (4): 375–484, ISSN 0021-7824, MR 0646366