Irreducibility of generalized Laguerre polynomials $L_n^{(1/2+u)}(x^2)$ with $-18 \leq u \leq -2$

DOI10.4064/AA170726-7-8zbMath1434.11214OpenAlexW2890363166MaRDI QIDQ4558624

Saranya G. Nair, Tarlok N. Shorey

Publication date: 22 November 2018

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa170726-7-8

zbMATH Keywords

primesNewton polygonsLaguerre polynomialsirreducibility

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Primes in congruence classes (11N13) Polynomials (irreducibility, etc.) (11R09) Distribution of primes (11N05)

Cites Work

• Solving exponential diophantine equations using lattice basis reduction algorithms
• Irreducibility of generalized Laguerre polynomials \(L_n^{(\frac{1}{2} + u)}(x)\) with integer \(u\)
• Number of prime divisors in a product of terms of an arithmetic progression
• Smooth values of some quadratic polynomials

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