Riemann Hypothesis for function fields
نویسنده
چکیده
1 1 Preliminaries 1 1.1 Function fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The zeta function . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Primes and Divisors . . . . . . . . . . . . . . . . . . . . 2 1.2.2 The Picard Group . . . . . . . . . . . . . . . . . . . . . . 5 1.2.3 Riemann-Roch . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 The zeta function 11 2.0.1 Convergence of the zeta function . . . . . . . . . . . . . . 16 2.0.2 A rational expression for zeta . . . . . . . . . . . . . . . 17 2.0.3 The functional equation . . . . . . . . . . . . . . . . . . 20 2.0.4 A corollary of the functional equation . . . . . . . . . . . 24 3 Riemann Hypothesis for function fields 25 3.1 The Weil bound . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Bombieri’s proof . . . . . . . . . . . . . . . . . . . . . . . . . . 29
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تاریخ انتشار 2009