zetafunction
Apr26-09, 08:32 AM
mi idea or conjecture is that
\sum _{p} exp(-sp) = \sum_{n>0} \frac{P(-n)}{n!}(-1)^{n} s^{n}
where P(-n) are the regularized values of the sum
\sum _{p}p^{-s}= P(s) extended to negative (integers) value of 's'
if the sum where over integers instead of just over primes i believe
\sum _{0\le n } exp(-sn) = \sum_{n>0} \frac{\zeta(-n)}{n!}(-1)^{n} s^{n}
i got the inspiration looking at Euler-maclaurin summation formula.
\sum _{p} exp(-sp) = \sum_{n>0} \frac{P(-n)}{n!}(-1)^{n} s^{n}
where P(-n) are the regularized values of the sum
\sum _{p}p^{-s}= P(s) extended to negative (integers) value of 's'
if the sum where over integers instead of just over primes i believe
\sum _{0\le n } exp(-sn) = \sum_{n>0} \frac{\zeta(-n)}{n!}(-1)^{n} s^{n}
i got the inspiration looking at Euler-maclaurin summation formula.