%0 Journal Article
%T Zeros of the Eta and Zeta Functions
%A John H. Heinbockel
%J Journal of Applied Mathematics and Physics
%P 256-266
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.131011
%X The eta function is examined over the critical strip <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mn>0</mn><mo>&#x003C;</mo><mi>&#x03C3;</mi><mo>&#x003C;</mo><mn>1</mn></mrow>
</math>

 and there is an investigation of the statement that all zeros of the zeta function must lie on the critical line <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>R</mi><mi>e</mi><mrow><mo>(</mo>
   <mi>s</mi>
  <mo>)</mo></mrow><mo>=</mo><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow>
  </mrow>
</math>

. A further investigation is made into the claim that there are no other zeros of the zeta or eta functions within the critical strip.
%K Riemann Hypothesis
%K Zeta Function Zeros
%K Dirichlet Eta Function Zeros
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140079