seminar:cp_p-adic_valuation_of_lucas_sequences

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seminar:cp_p-adic_valuation_of_lucas_sequences [2019/02/02 11:12] chatchawan |
seminar:cp_p-adic_valuation_of_lucas_sequences [2019/02/10 08:52] chatchawan |
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==== Abstract ==== | ==== Abstract ==== | ||

For relatively prime integers $P$ and $Q$, the Lucas sequence $(U_n)_{n\ge 0} = (U_n(P,Q))_{n\ge 0}$ is defined recursively by $U_0 = 0$, $U_1=1$, and $U_{n} = P\cdot U_{n-1}-Q\cdot U_{n-2}$ for $n\ge 2$. A recent work by Sanna has revealed an astounding formula for the powers of primes in the prime factorization of the Lucas sequence. Sanna's work is a generalization of the work by Lengyel who gave such formula only for the Fibonacci numbers which are the quintessential Lucas sequence with $a=1$ and $b=-1$. In this talk, I will discuss such formula and give applications which are recent joint work with Panraksa. | For relatively prime integers $P$ and $Q$, the Lucas sequence $(U_n)_{n\ge 0} = (U_n(P,Q))_{n\ge 0}$ is defined recursively by $U_0 = 0$, $U_1=1$, and $U_{n} = P\cdot U_{n-1}-Q\cdot U_{n-2}$ for $n\ge 2$. A recent work by Sanna has revealed an astounding formula for the powers of primes in the prime factorization of the Lucas sequence. Sanna's work is a generalization of the work by Lengyel who gave such formula only for the Fibonacci numbers which are the quintessential Lucas sequence with $a=1$ and $b=-1$. In this talk, I will discuss such formula and give applications which are recent joint work with Panraksa. | ||

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+ | ==== Slides ==== | ||

+ | {{ :seminar:p-adic_valuations_of_lucas_numbers.pdf |Slides from the talk}} | ||

Last modified: 2019/02/10 08:52