Fourier transform over finite field and identities between Gauss sums

• D. Kazhdan ^[1] ; A. Polishchuk ^[2]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] Boston University

     Boston University

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 9, Nº. 1, 2003, págs. 63-100
• Idioma: inglés
• DOI: 10.1007/s00029-003-0279-9
• Enlaces
  • Texto completo (pdf)
• Resumen

  • This paper is a sequel to [7]. Here we study identities for the Fourier transform of "elementary functions" over finite fields containing "exponentials" of rational monomial functions. It turns out that these identities are governed by monomial identities between Gauss sums. We show that similar to the case of complex numbers such identities correspond to linear relations between certain divisors on the space of multiplicative characters.