Equations in finite fields with restricted solution sets. I (Character sums)

K. Gyarmati, A. Sárközy

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In earlier papers, for "large" (but otherwise unspecified) subsets A, B of Z p and for h(x) Z p [x], Gyarmati studied the solvability of the equations a + b = h(x), resp. ab = h(x) with a A, b B, x Z p , and for large subsets A, B, C, D of Z p Sárközy showed the solvability of the equations a + b = cd, resp. ab + 1 = cd with a A, b B, c C, d D. In this series of papers equations of this type will be studied in finite fields. In particular, in Part I of the series we will prove the necessary character sum estimates of independent interest some of which generalize earlier results.

Original languageEnglish
Pages (from-to)129-148
Number of pages20
JournalActa Mathematica Hungarica
Volume118
Issue number1-2
DOIs
Publication statusPublished - Jan 1 2008

Keywords

  • Character sum
  • Equation
  • Finite field

ASJC Scopus subject areas

  • Mathematics(all)

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