mathematician23

3 ms·

1. 1.▲
   by mathematician23 10y ago

   One last point. The RH being true implies F(s) is analytic outside the critical line but within the critical strip. If we take what's called the contrapositive of this statement, then if we could somehow show F(s) is not analytic in th
2. 2.▲
   by mathematician23 10y ago

   There are many equivalent statements to the Riemann Hypothesis (RH) and statements that, if true, would imply the RH holds. But F(s) = zeta(2s)/zeta(s) being analytic in the critical strip, outside the critical line, DOES NOT imply the
3. 3.▲
   by mathematician23 10y ago

   A pole for F(s) means zeta(s) = 0 but zeta(2s) not=0 for some complex s. So yes, the zeros on the critical line appear as poles in F(s). Looking outside the critical line, at negative even integers, you will get 0/0 and using L-Hospita
4. 4.▲
   by mathematician23 10y ago

   The function he is trying to prove is analytic is a ratio of the zeta function at two places, so can be thought of as a ratio of two different complex functions. What if they both have a zero for some complex number s, i.e. zeta(2s)/ze