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Centralized variant of the Li criterion on functions fields
Institution:1. Department of Mathematics, University of Prishtina, Mother Theresa, no. 5, 10000 Prishtina, Kosovo;2. Faculty of Science of Monastir, Department of Mathematics, 5000 Monastir, Tunisia;1. University of Tartu, Institute of Computer Science, Tartu 50409, Estonia;2. 10 Anson Road, International Plaza, #38-16, 079903, Singapore;1. General Dynamics Advanced Information Systems, 8201 E. McDowell Rd, Scottsdale, AZ 85257, United States of America;2. School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ 85287, United States of America
Abstract:In this note, we study a Li-type criterion for the zeta function associated to the function field K of an arbitrary genus over a finite field of constants. First, we define two types of generalized Li-type coefficients and relate them with the Generalized Riemann Hypothesis. Furthermore, we provide different analytic representations for these coefficients and derive some interesting consequences.
Keywords:Function fields  Li's criterion
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