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 Apr 21 revised How to estimate a specific infinite sum added 185 characters in body Apr 20 revised Largest possible value of a sum deleted 126 characters in body Apr 20 comment How to estimate a specific infinite sum An estimate that is correct within a constant multiplicative factor (say a factor of 2) would be great but I am not sure what is achievable. Apr 20 comment How to estimate a specific infinite sum I used Mathematica. SiegelTheta[I*p/Pi, ConstantArray[0, Length@p]] where p is the matrix. Unfortunately this is very slow for anything but small matrices. In fact $n=10$ is about the maximum you can realistically do. Apr 20 comment How to estimate a specific infinite sum However, your upper bound for $n=10,k=5$ is around $1+ 11251.62470$ and your lower bound is around $1+0.5134138876*10^{-173}$. Apr 20 comment How to estimate a specific infinite sum I think the correct answer for $n=10, k=5$ is approx. $56.564$ . Apr 18 comment How to estimate a specific infinite sum Cross-posted to mathoverflow.net/questions/236572/… . Apr 17 revised How to estimate a specific infinite sum edited title Apr 17 revised How to estimate a specific infinite sum edited tags Apr 16 revised How to estimate a specific infinite sum added 60 characters in body Apr 15 awarded Peer Pressure Apr 13 revised How to estimate a specific infinite sum edited title Apr 13 asked How to estimate a specific infinite sum Apr 13 comment Largest possible value of a sum @robjohn Thank you but I worry that this approximation might not be good in high dimensions. Take the original LHS sum in the linked question math.stackexchange.com/questions/1699078/… . We could also approximate that by an integral but would it be a good approximation? Apr 13 revised Largest possible value of a sum added 124 characters in body Apr 13 comment Largest possible value of a sum Thank you. I will ask another question. Apr 13 comment Largest possible value of a sum Thank you. If the values in $M$ are bounded by $n$ in absolute value, what do you get as the upper bound? Apr 13 comment Largest possible value of a sum @YvesDaoust Thank you. I will ask another question having accepted the answer here. Apr 13 accepted Largest possible value of a sum Apr 13 comment Largest possible value of a sum @YvesDaoust Oh that's confusing. The sum comes from math.stackexchange.com/a/1699259/72724 and I thought that that sum converged if $M$ was positive definite. What have I got wrong?