| 11. | The "'local reciprocity law "'describes a canonical isomorphism
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| 12. | Despite his health, Eisenstein continued writing papers on quadratic partitions of prime numbers and the reciprocity laws.
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| 13. | Lemmermeyer states that there has been an explosion of interest in the rational reciprocity laws since the 1970s.
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| 14. | Her publications were mainly in number theory and computation, with emphasis on reciprocity laws, special primes, and congruences.
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| 15. | The latter dependence follows a reciprocity law, meaning that dislocations images become narrower inversely as the angular distance grows.
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| 16. | Therefore, the Artin reciprocity law can be interpreted as one of the main theorems of global class field theory.
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| 17. | But we are not supposed to use the Gaussian reciprocity law, only the Legendre symbol and some of its basic properties.
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| 18. | New York's governor, George E . Pataki, proposed a reciprocity law this year, but it failed to clear the state Legislature.
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| 19. | It combines with Pontryagin duality to give a clearer if more abstract formulation of the central result, the Artin reciprocity law.
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| 20. | Has many proofs ( some in exercises ) of both quadratic and higher-power reciprocity laws and a discussion of their history.
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