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Apr
21
revised How to estimate a specific infinite sum
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Apr
20
revised Largest possible value of a sum
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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
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Apr
17
revised How to estimate a specific infinite sum
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Apr
16
revised How to estimate a specific infinite sum
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Apr
15
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Apr
13
revised How to estimate a specific infinite sum
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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
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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?