solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看2887次
A representation theory approach to integral moments of L-functions over function fields. (arXiv:1810.01303v1 [math.NT])
来源于:arXiv
We propose a new heuristic approach to integral moments of L-functions over
function fields, which we demonstrate in the case of Dirichlet characters
ramified at one place (the function field analogue of the moments of the
Riemann zeta function, where we think of the character n^{it} as ramified at
the infinite place). We represent the moment as a sum of traces of Frobenius on
cohomology groups associated to irreducible representations. Conditional on a
hypothesis on the vanishing of some of these cohomology groups, we calculate
the moments of the L-function and they match the predictions of the
Conrey-Farmer-Keating-Rubinstein-Snaith recipe.
In this case, the decomposition into irreducible representations seems to
separate the main term and error term, which are mixed together in the long
sums obtained from the approximate functional equation, even when it is
dyadically decomposed. This makes our heuristic statement relatively simple,
once the geometric background is set up. We hope t 查看全文>>