Back to Search
Start Over
Traces, high powers and one level density for families of curves over finite fields.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Sep2018, Vol. 165 Issue 2, p225-248. 24p. - Publication Year :
- 2018
-
Abstract
- The zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix Θ C . We develop and present a new technique to compute the expected value of tr(Θ C n ) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [ Rud10 ] and Chinis [ Chi16 ]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [ BDF+16 ] and [ Zha ]. We extend [ BDF+16 ] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L -functions L (1/2 + it , χ). As applications, we compute the one-level density for hyperelliptic curves, cyclic ℓ-covers, and cubic non-Galois covers. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE fields
*ZETA functions
*POLYNOMIALS
*EXPECTED returns
*MODULI theory
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 165
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 130988324
- Full Text :
- https://doi.org/10.1017/S030500411700041X