Divisibility properties of hypergeometric polynomials (Q2869139)
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scientific article; zbMATH DE number 6242437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Divisibility properties of hypergeometric polynomials |
scientific article; zbMATH DE number 6242437 |
Statements
3 January 2014
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hypergeometric polynomials
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irreducibility
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\(p\)-adic Newton polygons
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gaps between primes
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Divisibility properties of hypergeometric polynomials (English)
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The hypergeometric polynomials \(g_{a,b,c}(x)\) considered in this paper appear by truncating the infinite series given by generalized hypergeometric functions of type \({}_2F_2(a,1;b,c,x)\). These polynomials generalize the Laguerre polynomials. The authors give effective upper bounds for the degree of divisors (over the field of rational numbers) of some families of these hypergeometric polynomials. The proofs use in particular very precise numerical estimates. Moreover, better results are obtained assuming the \(abc\)-conjecture.
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