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Displaying similar documents to “Class invariants and cyclotomic unit groups from special values of modular units”

Computations with Witt vectors of length 3

Luís R. A. Finotti (2011)

Journal de Théorie des Nombres de Bordeaux

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In this paper we describe how to perform computations with Witt vectors of length 3 in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the j -invariant of the canonical lifting as a function on the j -invariant of the ordinary elliptic curve in characteristic p .

Fibonacci numbers and Fermat's last theorem

Zhi-Wei Sun (1992)

Acta Arithmetica

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Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, F n + 1 = F ₙ + F n - 1 ( n ≥ 1 ) . It is well known that F p - ( 5 / p ) ≡ 0 ( m o d p ) for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether p ² | F p - ( 5 / p ) is always impossible; up to now this is still open. In this paper the sum ∑ k ≡ r ( m o d 10 ) n k is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient F p - ( 5 / p ) / p and a criterion for the relation p | F ( p - 1 ) / 4 (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative...