“Mahler-Lech Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Mahler-Lech Theorem

释义

Mahler-Lech Theorem

Let be a Field of Characteristic 0 (e.g., the rationals ) andlet be a Sequence of elements of which satisfies a difference equation of the form

where the Coefficients

are fixed elements of

. Then, for any

, we have either

for only finitely many values of

, or

for the values of

in someArithmetic Progression.

The proof involves embedding certain fields inside the p-adic Number for somePrime , and using properties of zeros of Power series over (Strassman's Theorem).

See also Arithmetic Progression, p-adic Number, Strassman's Theorem

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