ANOTHER PROOF OF SPIRA%26apos;S INEQUALITY AND ITS APPLICATION TO THE RIEMANN HYPOTHESIS

作者：Nazardonyavi Sadegh^*; Yakubovich Semyon

来源：Journal of Mathematical Inequalities, 2013, 7(2): 167-174.

DOI：10.7153/jmi-07-16

• Riemann zeta-function
• size of the Riemann zeta-function
• critical strip

By using new inequalities involving powers of rational functions, we give another proof of an important Spira%26apos;s relation for the Riemann zeta-function vertical bar zeta(1 s)vertical bar %26lt;= vertical bar zeta(s)vertical bar in the strip 0 %26lt; Rs %26lt; 1/2, vertical bar Is vertical bar %26gt;= 12. Moreover, we establish a sufficient condition of the validity of the Riemann hypothesis in terms of the derivative of vertical bar zeta(s)vertical bar(2) with respect to Rs and conjecture its necessity.

• 出版日期2013-6