Waring–Goldbach Problem of Even Powers in Short Intervals
Waring–Goldbach Problem of Even Powers in Short Intervals
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> …