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Article overview
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On restricted averages of Dedekind sums | | Paolo Minelli
; Athanasios Sourmelidis
; Marc Technau
; | | Date: |
1 Jan 2023 | | Abstract: | We investigate the averages of Dedekind sums over rational numbers in the set
$$mathscr{F}_alpha(Q):={, {v}/{w}in mathbb{Q}: 0<wleq Q,}cap [0,
alpha)$$
for fixed $alphaleq 1/2$.
In previous work, we obtained asymptotics for $alpha=1/2$, confirming a
conjecture of Ito in a quantitative form.
In the present article we extend our former results, first to all fixed
rational $alpha$ and then to almost all irrational $alpha$.
As an intermediate step we obtain a result quantifying the bias occurring in
the second term of the asymptotic for the average running time of the
extit{by-excess} Euclidean algorithm, which is of independent interest. | | Source: | arXiv, 2301.00441 | | Services: | Forum | Review | PDF | Favorites | |
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