On Tue, Jun 1, 2010 at 10:58 AM, Robert Bradshaw <rober...@math.washington.edu> wrote: > On Jun 1, 2010, at 8:13 AM, Anne Driver wrote: > >> Hello, >> >> I am new to this list, and relatively new to Sage. I'm puzzled by the >> logic of one part of Sage though. >> >> Although I don't have access to Mathematica at the minute on this >> computer, I know if I compute the first zero, I get something like >> >> In[1] = ZetaZero[1] //N (to get a numerical value) >> Out[1] = 1/2 + I*14.134... >> >> Trying this in Sage, I get: >> >> sage: lcalc.zeros(1) >> [14.1347251] >> >> >> Why does Sage not do the sensible thing like Mathematica and return the >> complex number 0.5 + I 14.1347251 ? It would seem much more logical. >> >> Of course, it is not proven that the real part is 1/2, so how would the >> case be handled if a root was not found to have a real part of 1/2 ? > > I believe both algorithms assume the Riemann hypothesis in computing them > (otherwise, for example, it would be ambiguous to talk about the n-th zero > anyways).
Often such computations actually prove the Riemann hypothesis up to a given height (see, e.g., http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf) I've cc'd Mike Rubinstein, so he can respond if he wants, since I'm not sure lcalc is actually doing this or not. -- William > I would guess the reason that lcalc returns the imaginary part > only is that otherwise the first thing one would do to actually do anything > interesting with this data would be to take the imaginary part, so this just > saves the effort and overhead. > > - Robert > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
