TITLE

On Mean Values of Character Sums

AUTHOR(S)
Zai Zhao Meng
PUB. DATE
April 2006
SOURCE
Acta Mathematica Sinica;Apr2006, Vol. 22 Issue 2, p561
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We use the resultant of two polynomials to discuss the roots of congruences, and then we improve the result of Burgess on the mean values of character sums in the case r = 3. Finally, we give a new estimate for the mean values of character sums in the case r = 4.
ACCESSION #
20032441

 

Related Articles

  • COUNTEREXAMPLES TO TISCHLER'S STRONG FORM OF SMALE'S MEAN VALUE CONJECTURE. JEREMY T. TYSON // Bulletin of the London Mathematical Society;Jan2005, Vol. 37 Issue 1, p95 

    Smale's mean value conjecture asserts that $\min_\theta |P(\theta)/\theta| \le K|P'(0)|$ for every polynomial $P$ of degree $d$ satisfying $P(0)\,{=}\,0$, where $K\,{=}\,(d-1)/d$ and the minimum is taken over all critical points $\theta$ of $P$. A stronger conjecture due to Tischler asserts that...

  • Converses of Jessen's inequality on time scales. Barić, J.; Bohner, M.; Jakšić, R.; Pečarić, J. // Mathematical Notes;Jul2015, Vol. 98 Issue 1/2, p11 

    In this paper, some converses of Jessen's inequality, in terms of the time scale calculus, are proved. The obtained results are used to derive new converse inequalities for generalized means, power means and Hölder's inequality.

  • On the mean value of the function $$ {\bar{S}_k}(n) $$. Varbanets, P.D.; Kirbat, S. // Ukrainian Mathematical Journal;Sep2011, Vol. 63 Issue 4, p516 

    An asymptotic formula is constructed for the mean value of the function $$ {\bar{S}_k}(n) $$ dual to the Smarandache function S ( n). The O- and O-estimates for the second moment of the remainder are obtained.

  • Some inequalities for polynomials and rational functions associated with lemniscates. Dubinin, V. // Journal of Mathematical Sciences;Aug2013, Vol. 193 Issue 1, p45 

    Inequalities for the area of a lemniscate and inequalities for polynomials in a lemniscate containing no critical points distinct from zeros are presented. Also, multipoint distortion estimates on boundaries of lemniscates are proved. Some open problems are discussed. One of them is connected...

  • A Note on the Mean Value of Numbers of the Solutions ofxa = 1(modn). Yu, Xiu // Acta Mathematica Sinica;Nov2004, Vol. 20 Issue 6, p1095 

    LetT=T(p,q, a) be the number of solutions of the congruencexa = 1 (modp?q?). LetAandBbe sets of primes satisfying x1 < p ≤ x2 and y1 < q ≤ y2, respectively. A mean value estimation ofis given.

  • On the Sixth Power Mean Value of the Generalized Three-Term Exponential Sums. Yahui Yu; Wenpeng Zhang // Abstract & Applied Analysis;2014, p1 

    The main purpose of this paper is using the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean value of the generalized three-term exponential sums and give an exact computational formula for it.

  • A new mean-value result for Dirichlet L-functions and polynomials. HARMAN, GLYN; WATT, NIGEL; KAM WONG // Quarterly Journal of Mathematics;Sep2004, Vol. 55 Issue 3, p307 

    Watt's result on upper bounds for the mean value

  • Using Generalizability Theory to Estimate the Dependability of Aggregate-level Variables. O'Brien, Robert M. // Quality & Quantity;Feb84, Vol. 18 Issue 2, p193 

    In this article, some basic components of generalizability theory are briefly outlined. Then its usefulness to social scientists outside the area of psychology is demonstrated by showing how it can be used to generate measures of dependability (reliability) for two distinct types of...

  • The Uncertainty Reduction for the Refined Sample Mean of Combined Quantities. Wen-Hui Lo; Sin-Horng Chen // International Journal of Applied Mathematics;2009, Vol. 39 Issue 3, p192 

    Sampling plans for middle or small sample size are often taken when the available data is not large enough. In this paper, a new quantile-based maximum likelihood estimation (QMLE) method for mean value estimation of a quasi-normal distribution is proposed. It takes the two endpoints of range as...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics