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- W3080997446 abstract "For any prime $p$, let $y(p)$ denote the smallest integer $y$ such that every reduced residue class $pmod p$ is represented by the product of some subset of ${1,dots,y}$. It is easy to see that $y(p)$ is at least as large as the smallest quadratic nonresidue $pmod p$; we prove that $y(p) ll_varepsilon p^{1/(4 sqrt e)+varepsilon}$, thus strengthening Burgess's classical result. This result is of intermediate strength between two other results, namely Burthe's proof that the multiplicative group $pmod p$ is generated by the integers up to $O_varepsilon(p^{1/(4 sqrt e)+varepsilon}$, and Munsch and Shparlinski's result that every reduced residue class $pmod p$ is represented by the product of some subset of the primes up to $O_varepsilon(p^{1/(4 sqrt e)+varepsilon}$. Unlike the latter result, our proof is elementary and similar in structure to Burgess's proof for the least quadratic nonresidue." @default.
- W3080997446 created "2020-09-01" @default.
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- W3080997446 date "2021-01-13" @default.
- W3080997446 modified "2023-09-27" @default.
- W3080997446 title "Subproducts of small residue classes" @default.
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- W3080997446 doi "https://doi.org/10.4153/s0008439521000011" @default.
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