Geodesic
A function field analog of Jacobi’s theorem on sums of squares and its moments
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 667-683

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DOI

In this article, we establish a function field analog of Jacobi’s theorem on sums of squares and analyze its moments. Our approach involves employing two distinct techniques to derive the main results concerning asymptotic formulas for the moments. The first technique utilizes Dirichlet series framework to derive asymptotic formulas in the limit of large finite fields, specifically when the characteristic of $\mathbb {F}_q[T]$ becomes large. The second technique involves effectively partitioning the set of polynomials of a fixed degree, providing asymptotic formulas in the limit of large polynomial degree.
DOI : 10.4153/S0008439525000025
Mots-clés : Sums of squares, quadratic forms, Jacobi’s theorem, number of representations, polynomial rings 
Kuo, Wentang; Liu, Yu-Ru; Totani, Yash. A function field analog of Jacobi’s theorem on sums of squares and its moments. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 667-683. doi: 10.4153/S0008439525000025
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     title = {A function field analog of {Jacobi{\textquoteright}s} theorem on sums of squares and its moments},
     journal = {Canadian mathematical bulletin},
     pages = {667--683},
     year = {2025},
     volume = {68},
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     doi = {10.4153/S0008439525000025},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000025/}
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