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Explicit Representations of Faber Polynomials form-Cusped Hypocycloids

✍ Scribed by Matthew X. He

Book ID
102577666
Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
342 KB
Volume
87
Category
Article
ISSN
0021-9045

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✦ Synopsis

Let F n (z) be Faber polynomials associated with an m-cusped hypocycloid. We derive an explicit algebraic expression for F n (z) via a Cauchy integral formula. Using a differential equation of F n (z), we precisely represent F n (z) in terms of generalized hypergeometric functions.

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Let S wΓΎ2 be the vector space of cusp forms of weight w ΓΎ 2 on the full modular group, and let S Γƒ wΓΎ2 denote its dual space. Periods of cusp forms can be regarded as elements of S Γƒ wΓΎ2 . The Eichler-Shimura isomorphism theorem asserts that odd (or even) periods span S Γƒ wΓΎ2 . However, periods are