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- W2983417405 abstract "We study the joint distribution of the solutions to the equation $$gh=x$$ in $$G(mathbb {F}_p)$$ as $$prightarrow infty $$, for any fixed $$xin G(mathbb {Z})$$, where $$G={text {GL}}_n$$, $${text {SL}}_n$$, $${text {Sp}}_{2n}$$ or $${text {SO}}_{n}^pm $$. In the special linear case, this answers in particular a question raised by Hu and Li, and improves their error terms. Similar results are derived in certain subgroups, and when the entries of g, h lie in fixed intervals. The latter shows for example the existence of $$gin {text {GL}}_n(mathbb {F}_p)$$ such that $$g,g^{-1}$$ have all entries in $$[0, c_np^{1-1/(2n^2+2)+varepsilon }]$$ for some absolute constant $$c_n>0$$. The key for these results is to use Deligne’s extension of the Weil conjectures on a sheaf on G, along with the stratification theorem of Fouvry, Katz and Laumon, instead of reducing to bounds on classical Kloosterman sums." @default.
- W2983417405 created "2019-11-22" @default.
- W2983417405 creator A5063921334 @default.
- W2983417405 date "2019-11-07" @default.
- W2983417405 modified "2023-10-17" @default.
- W2983417405 title "Joint distribution of inverses in matrix groups over finite fields" @default.
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- W2983417405 doi "https://doi.org/10.1007/s40993-019-0176-8" @default.
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