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• W3124751536 abstract "We compute the variances of sums in arithmetic progressions of generalised k-divisor functions related to certain L-functions in $mathbb{F}_q(t)$, in the limit as $qtoinfty$. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when $qtoinfty$, in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual $k$-divisor function, when the L-function in question has degree one. They illustrate the role played by the degree of the L-functions; in particular, we find qualitatively new behaviour when the degree exceeds one. Our calculations apply, for example, to elliptic curves defined over $mathbb{F}_q(t)$, and we illustrate them by examining in some detail the generalised $k$-divisor functions associated with the Legendre curve." @default.
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• W3124751536 date "2019-02-13" @default.
• W3124751536 modified "2023-10-18" @default.
• W3124751536 title "Variance of arithmetic sums and L-functions in 𝔽q[t]" @default.
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• W3124751536 doi "https://doi.org/10.2140/ant.2019.13.19" @default.
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