Waring–Goldbach Problem of Even Powers in Short Intervals

Abstract

In this paper, we study the average behaviour of the representations of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>n</mi> <mo>=</mo> <msubsup> <mi>p</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mn>2</mn> <mn>4</mn> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mn>3</mn> <mn>4</mn> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mn>4</mn> <mi>k</mi> </msubsup> </math> over short intervals for <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>k</mi> <mo>≥</mo> <mn>4</mn> </math> , where <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>p</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </math> are prime numbers. This improves the previous results.

Locations

• Journal of Mathematics - View - PDF
• DOAJ (DOAJ: Directory of Open Access Journals) - View