Weil conjectures Conjecture

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in mathematics, weil conjectures highly influential proposals andré weil (1949) on generating functions (known local zeta-functions) derived counting number of points on algebraic varieties on finite fields.


a variety v on finite field q elements has finite number of rational points, points on every finite field q elements containing field. generating function has coefficients derived numbers nk of points on (essentially unique) field q elements.


weil conjectured such zeta-functions should rational functions, should satisfy form of functional equation, , should have zeroes in restricted places. last 2 parts quite consciously modeled on riemann zeta function , riemann hypothesis. rationality proved dwork (1960), functional equation grothendieck (1965), , analogue of riemann hypothesis proved deligne (1974)







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