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Remarks on the Pólya–Vinogradov Inequality

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Published/Copyright: August 4, 2011
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Integers
From the journal Volume 11 Issue 4

Abstract

We establish a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently.

Keywords.: Dirichlet Character; Gauss Sum; Pólya–Vinogradov Inequality
Received: 2010-01-25
Accepted: 2010-07-10
Published Online: 2011-08-04
Published in Print: 2011-August

© de Gruyter 2011

Articles in the same Issue

  1. The Number of Solutions of λ(x) = n
  2. Monochromatic Sums Equal to Products in ℕ
  3. On the Sum of Reciprocal Generalized Fibonacci Numbers
  4. Recursively Self-Conjugate Partitions
  5. Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
  6. Algebraic Proof for the Geometric Structure of Sumsets
  7. An Erdős–Fuchs Type Theorem for Finite Groups
  8. Coincidences of Catalan and q-Catalan Numbers
  9. Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
  10. Perfect Numbers with Identical Digits
  11. Remarks on the Pólya–Vinogradov Inequality
  12. Heights of Divisors of xn – 1
  13. Bernoulli Numbers and Generalized Factorial Sums
  14. Witten Volume Formulas for Semi-Simple Lie Algebras
https://doi.org/10.1515/integ.2011.039
Keywords for this article
Dirichlet Character; Gauss Sum; Pólya–Vinogradov Inequality

Articles in the same Issue

  1. The Number of Solutions of λ(x) = n
  2. Monochromatic Sums Equal to Products in ℕ
  3. On the Sum of Reciprocal Generalized Fibonacci Numbers
  4. Recursively Self-Conjugate Partitions
  5. Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
  6. Algebraic Proof for the Geometric Structure of Sumsets
  7. An Erdős–Fuchs Type Theorem for Finite Groups
  8. Coincidences of Catalan and q-Catalan Numbers
  9. Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
  10. Perfect Numbers with Identical Digits
  11. Remarks on the Pólya–Vinogradov Inequality
  12. Heights of Divisors of xn – 1
  13. Bernoulli Numbers and Generalized Factorial Sums
  14. Witten Volume Formulas for Semi-Simple Lie Algebras
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