Notes on G2, determinants, and equidistribution

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We determine the exact shape of the G2 equidistribution law for the one parameter family of exponential sums over Fp ×, ∑ x mod p, x≠0 χ2(x) exp(2πi(x7+tx)/p). Here χ2(x) denotes the quadratic character (x/p), t in Fp, is the parameter, and p is any prime other than 2 or 7. This answers a question raised in Keating et al. (J. Phys. A Math. Gen. 36 (2003) 2943, footnote 3) and in Serre (pers. commun., March 7, 2002). We also analyze the analogous families when 7 is replaced by any odd integer n≥3.

Original languageEnglish (US)
Pages (from-to)221-269
Number of pages49
JournalFinite Fields and their Applications
Issue number2
StatePublished - Apr 2004

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Algebra and Number Theory
  • General Engineering
  • Applied Mathematics


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