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Numerical modular symbols for elliptic curves. (English) Zbl 1453.11080

Summary: We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementations as the conductor of the curve increases.

MSC:

11G05 Elliptic curves over global fields
11-04 Software, source code, etc. for problems pertaining to number theory
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11Y16 Number-theoretic algorithms; complexity
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References:

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