TY  - JOUR
A1  - Gauthier, P. M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On the instability of the Riemann hypothesis for curves over finite fields
T2  - Journal of approximation theory
N2  - We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) an analog of the Riemann hypothesis. In the other direction, it is possible to approximate holomorphic functions by simple manipulations of such a zeta-function. No number theory is required to understand the theorems and their proofs, for it is known that the zeta-functions of curves over finite fields are very explicit meromorphic functions. We study the approximation properties of these meromorphic functions.
KW  - Zeta-function
Y1  - 2012
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/36012
SN  - 0021-9045
VL  - 164
IS  - 4
SP  - 504
EP  - 515
PB  - Elsevier
CY  - San Diego
ER  -