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comment Learning the exponents in a sum of two modular roots of unity
Yes, this paper on lens spaces: arxiv.org/abs/1509.02887
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accepted Learning the exponents in a sum of two modular roots of unity
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comment Learning the exponents in a sum of two modular roots of unity
If you could send me your name by private e-mail, I'd be more than happy to thank you for this, even though you just basically caught me in a mistake.
Aug
28
comment Learning the exponents in a sum of two modular roots of unity
At least if you fix q, then problem cannot be any easier than discrete logarithm. If you know b, then it simply is the discrete logarithm problem.
Aug
28
comment Learning the exponents in a sum of two modular roots of unity
Duh, I think you're right, this works. I'm not entirely sure why I missed it, other than that I was moving too quickly. I actually had a different question at first that I simplified to this one with a similar trick.
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28
revised Learning the exponents in a sum of two modular roots of unity
added 39 characters in body
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comment Learning the exponents in a sum of two modular roots of unity
Think about it. If $q > n^3$, then you expect all $n$ values of $f$ to be distinct. The Weil estimate is generally in the ballpark of heuristic counting.
Aug
28
comment Learning the exponents in a sum of two modular roots of unity
If $m < q^{1/4}$, then $q$ has at most 4/3 as many digits as $n$.