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Explicit results on the arithmetic of curves of higher genus. (English. Russian original) Zbl 0597.14027
Russ. Math. Surv. 40, No. 4, 43-48 (1985); translation from Usp. Mat. Nauk 40, No. 4(244), 43-47 (1985).
This is a survey of the problem of determining integer or rational solutions of algebraic equations. Various old results are discussed with special attention to the consideration of whether the proof gives ineffective solutions (only finiteness of solutions) or effective but infeasible solutions (gives known but astronomical bounds) or feasible solutions (gives a reasonable bound and algorithm to determine the solutions).
Reviewer: A.Sathaye
MSC:
14H45 Special algebraic curves and curves of low genus
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14H52 Elliptic curves
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