Equations over Finite Fields: An Elementary Approach

a₁ absolute variety absolutely irreducible additive character algebraic extension algebraic set algebraically independent b₁ Chapter character of F character sums coefficients in F common zero COROLLARY curve d₁ defined deg f denote elements equations equivalent exponent f₁ factor field F finite field follows form of degree function field g₁ h₁ Hence homomorphism hypersurface hypothesis identically zero induction irreducible polynomial isomorphism Lemma 3A Let f linear manifold linearly disjoint linearly independent modulo n-tuples non-trivial non-zero number of solutions number of zeros obtain polynomial f polynomial of degree prime ideal proof of Theorem proved q Let rational functions satisfies Stepanov summand Suppose f Theorem 1A total degree transcendence degree u₁ V₁ variables whence X₁ XE F q Y₁ zeros of f αΕΙ ΕΩ ψ≠ψο