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تسجيل مستخدم جديدComputing $L$-functions and semistable reduction of superelliptic curves
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We give an explicit description of the stable reduction of superelliptic curves of the form $y^n=f(x)$ at primes $p$ whose residue characteristic is prime to the exponent $n$. We then use this description to compute the local $L$-factor of the curve and the exponent of conductor at $p$.
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We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.
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