Weird approximate number values on Maass forms

[Victor Kisly]

I was browsing through Maass forms and noticed on some pages that coefficients have weird approximate values, e.g. here:
a5=−1.80241357±2.1;  for a value that's given with 8 digits of precision it doesn't make sense for the error to be 2.1. Same situation with other coefficients. This appears to be the case with multiple Maass forms around 14, as I looked through multiple and all of them had this issue. It could be that I'm missing something about how the values are supposed to be displayed.

[David Roe]

Hi Victor,

See Remark 3 in David Lowry-Duda's paper about the computation.  I've CCed him in case he has more comments.  Perhaps we need to explain the precision conventions in the various knowls associated to these real values.

David

On Thu, Oct 30, 2025 at 10:43 AM Victor Kisly <kisly...@gmail.com> wrote:

I was browsing through Maass forms and noticed on some pages that coefficients have weird approximate values, e.g. here:
a5=−1.80241357±2.1;  for a value that's given with 8 digits of precision it doesn't make sense for the error to be 2.1. Same situation with other coefficients. This appears to be the case with multiple Maass forms around 14, as I looked through multiple and all of them had this issue. It could be that I'm missing something about how the values are supposed to be displayed.

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[David Roe]

Yes, that's my understanding.  The error bar gives the interval within which the result has been proven to lie, but heuristically we believe we know it to much higher accuracy.

David

On Thu, Oct 30, 2025 at 11:21 AM Victor Kisly <kisly...@gmail.com> wrote:

Thanks David. From this I understand these values should be treated as correct up until the specified precision, with the extra digits being "likely" correct.

[Victor Kisly]

Thanks David. From this I understand these values should be treated as correct up until the specified precision, with the extra digits being "likely" correct.

On Thu, Oct 30, 2025 at 5:57 PM David Roe <roed...@gmail.com> wrote: