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March 2, 2026Demonstratio Mathematica0 citationsOpen Access

On the 2 k -th power mean of the quadratic character sums of the polynomials

WZWenpeng ZhangLWL Wang

Key Points

  • The central aim is to explore the 2k-th power mean of quadratic character sums of polynomials using known results from elliptic curves.
  • Utilized known results on elliptic curves over fixed prime fields.
  • Applied elementary methods in analysis of quadratic character sums.
  • Developed exact calculation formulas and a general asymptotic formula.
  • Provided exact formulas for the 2k-th power mean of quadratic character sums.
  • Derived a general asymptotic formula applicable to these sums.

Abstract

Abstract The main aim of this paper is using the already know results on the elliptic curve over a fixed prime field and the elementary methods to study the calculating problem of one kind 2 k -th power mean of the quadratic character sums of the polynomials, and give some exact calculating formulas and a general asymptotic formula for them.

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Cite This Study

Zhang et al. (2026) studied this question.

synapsesocial.com/papers/69a52d9af1e85e5c73bf0a6bhttps://doi.org/10.1515/dema-2025-0219
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A Classical Introduction to Modern Number Theory1982 · 2,195 citations
  2. 2On Some Exponential Sums1948 · 800 citations
  3. 3How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies1968 · 154 citations
  4. 4Introduction to Analytic Number Theory1976 · 1,597 citations
  5. 5On the multiplication of Dirichlet series1962 · 3 citations