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Some arithmetic properties of the Legendre polynomials

Published online by Cambridge University Press:  24 October 2008

L. Carlitz
L. Carlitz
Affiliation:
Duke UniversityNorth Carolina
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Extract

1. Good (4) has proved the formula

where Pn(x) is the Legendre polynomial of degree n and t is any integer greater than n. The form of the right-hand side suggests that (1) may be of use in deriving arithmetic properties of Pn(x).

Elsewhere (1) the writer indicated a connexion between divisibility properties of Pm(a) for special values of a and the complex multiplication of elliptic functions. If p = 2m + 1 is an odd prime, put

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 265 - 268
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

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