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- W2951691710 abstract "Using the sieve for Frobenius, we show that, in a certain sense, the roots of the L-functions of most algebraic curves over finite fields do not satisfy any non-trivial (linear or multiplicative) rational dependency relations. This can be seen as an analogue of conjectures of linear independence among ordinates of zeros of L-functions over number fields. As a corollary, we find, for most pairs of distinct algebraic curves over a finite field, the limiting distribution of the (suitably normalized) difference between the number of rational points over extensions of the ground field. The method of proof also emphasizes the relevance of Random Matrix models for this type of arithmetic questions. We also describe an alternative approach, which relies on Serre's theory of Frobenius tori, and we give a number of examples." @default.
- W2951691710 created "2019-06-27" @default.
- W2951691710 creator A5072422353 @default.
- W2951691710 date "2008-07-14" @default.
- W2951691710 modified "2023-09-27" @default.
- W2951691710 title "The large sieve, monodromy and zeta functions of algebraic curves, II: independence of the zeros" @default.
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- W2951691710 hasPublicationYear "2008" @default.
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