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We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an $ℛ$ -orthomorphism. Examples of $ℛ$ -orthomorphisms are given.

Introduction to Kloostermania

M. N. Huxley (1985)

Banach Center Publications

Large families of pseudorandom binary sequences constructed by using the Legendre symbol

Huaning Liu, Jing Gao (2012)

Acta Arithmetica

Large sieve inequality with characters to square moduli

Liangyi Zhao (2004)

Acta Arithmetica

Local problems with primes I.

Alberto Perelli (1989)

Journal für die reine und angewandte Mathematik

Majoration de sommes exponentielles attachées aux hypersurfaces diagonales

Gérard Laumon (1983)

Annales scientifiques de l'École Normale Supérieure

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Density theorems for exceptional eigenvalues of the Laplacian for congruence groups

Der Paleysche Satz über Charaktere.

Diagonal cubic equations. II

Dirichlet character sums

Durchschnitte von Pjateckij-Shapiro-Folgen.

Estimates of character sums with exponential function

Estimation Optimale de sommes Exponentielles

Existence of Good Lattice Points in the Sense of Hlawka.

Exponential sums associated with algebraic number fields.

Exponential sums on (Gm)n.

Fourth power mean of character sums

Gleichverteilung und das Konvergenzverhalten von Potenzreihen am Rande des Konvergenzkreises.

Improvement on Davenport's iterative method and new results in additive number theory III

Improvement on Davenport's iterative method and new results in additive number theory, I

Incomplete character sums and a special class of permutations