COMPLEX MOMENTS AND THE DISTRIBUTION OF VALUES OF OVER FUNCTION FIELDS WITH APPLICATIONS TO CLASS NUMBERS
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Bibliographic record
Abstract
In this paper we investigate the moments and the distribution of , where varies over quadratic characters associated to square-free polynomials of degree over , as . Our first result gives asymptotic formulas for the complex moments of in a large uniform range. Previously, only the first moment has been computed due to the work of Andrade and Jung. Using our asymptotic formulas together with the saddle-point method, we show that the distribution function of is very close to that of a corresponding probabilistic model. In particular, we uncover an interesting feature in the distribution of large (and small) values of , which is not present in the number field setting. We also obtain -results for the extreme values of , which we conjecture to be the best possible. Specializing and making use of one case of Artin's class number formula, we obtain similar results for the class number associated to . Similarly, specializing to we can appeal to the second case of Artin's class number formula and deduce analogous results for , where is the regulator of .
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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