Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • On Incomplete Character Sums to a Prime-Power Modulus

  • J. H. H. Chalk
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 3 / 01 September 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 257-266
    Print publication:
    01 September 1987
    • Article
      • You have access
    • PDF
    • Export citation

  • Let x denote a primitive character to a prime-power modulus k = pα. The expected estimate

    for the incomplete character sum has been established for r = 1 and 2 by D. A. Burgess and recently, he settled the case r = 3 for all primes p < 3, (cf. [2] for the proof and for references). Here, a short proof of the main inequality (Theorem 2) which leads to this result is presented; the argument being based upon my characterization in [3] of the solution-set of a related congruence.

  • On a Congruence Related to Character Sums

  • J. H. H. Chalk
  • Journal:
    Canadian Mathematical Bulletin / Volume 28 / Issue 4 / 01 December 1985
    Published online by Cambridge University Press:
    20 November 2018, pp. 431-439
    Print publication:
    01 December 1985
    • Article
      • You have access
    • PDF
    • Export citation

  • If χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the type

    f(x)g'(x) - f'(x)g(x) ≡ 0(pα),

    where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.