bibkey: lidlniederreiter1997finitefields authors: Rudolf Lidl; Harald Niederreiter year: 1997 title: Finite Fields doi: null url: https://doi.org/10.1017/CBO9780511525790 claim: Character-sum methods over finite fields, including quadratic-character evaluations used for shifted-square sums. strata_touched:

• D5/S3/Arith/FiniteFieldQuadraticCharacterSum license: citation-only triage: anchor

Finite Fields

Lidl and Niederreiter’s second edition is the classical reference for finite fields and their character sums. This note records the literature anchor for the shifted quadratic-character identity deposited in D5/S3/Arith/FiniteFieldQuadraticCharacterSum.

The repository theorem is the explicit odd-characteristic identity ∑ x, χ(x²-a) = -1 for a ≠ 0; its point-counting proof is checked in Lean here. The note does not claim that the cited book contains this exact Lean formulation or the repository’s chosen bijection.

Source boundary

The cited discussion is in the character-sums material of the second edition. No page or theorem number is asserted here; the formal declaration and its finite-field hypotheses are the repository’s machine-checked contribution.

Verified locator

• Cambridge University Press DOI landing page: https://doi.org/10.1017/CBO9780511525790