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The American Mathematical Monthly Volume 107, 2000 - Issue 9
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Original Articles

The Factorial Function and Generalizations

Manjul Bhargava 52 Stewart Avenue, Bethpage, [email protected]View further author information
Pages 783-799 | Published online: 23 Apr 2018

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Read on this site (6)

Wataru Takeda. (2023) On the Bhargava factorial of polynomial maps. Communications in Algebra 51:7, pages 3124-3133.
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Maiyu Diaz. (2023) Asymptotics on a Class of Legendre Formulas. The American Mathematical Monthly 130:1, pages 20-34.
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Jonathan M. Borwein & Robert M. Corless. (2018) Gamma and Factorial in the Monthly. The American Mathematical Monthly 125:5, pages 400-424.
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Paul-Jean Cahen, Jean-Luc Chabert & Kiran S. Kedlaya. (2017) Bhargava's Early Work: The Genesis of P-Orderings. The American Mathematical Monthly 124:9, pages 773-790.
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Keith Johnson & Kira Scheibelhut. (2016) Rational Polynomials That Take Integer Values at the Fibonacci Numbers. The American Mathematical Monthly 123:4, pages 338-346.
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Paul-Jean Cahen & Jean-Luc Chabert. (2016) What You Should Know About Integer-Valued Polynomials. The American Mathematical Monthly 123:4, pages 311-337.
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Articles from other publishers (24)

Jeffrey C. Lagarias & Wijit Yangjit. (2024) The factorial function and generalizations, extended. Journal of Number Theory 259, pages 131-170.
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Anna Szumowicz. 2023. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory 427 442 .
Asmita C. Sodhi. 2023. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory 405 425 .
David Adam & Jean-Luc Chabert. 2023. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory. Algebraic, Number Theoretic, and Topological Aspects of Ring Theory 9 35 .
Wataru Takeda. (2021) On the finiteness of solutions for polynomial-factorial Diophantine equations. Forum Mathematicum 33:2, pages 361-374.
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Xiumei Li & Min Sha. (2019) Polynomial functions in the residue class rings of Dedekind domains. International Journal of Number Theory 15:07, pages 1473-1486.
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David Adam. (2018) Polynômes à valeurs entières sur des ensembles invariants par rotation. Journal of Number Theory 186, pages 417-438.
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Paul-Jean Cahen & Jean-Luc Chabert. (2018) Test sets for polynomials: n-universal subsets and Newton sequences. Journal of Algebra 502, pages 277-314.
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Jean-Luc Chabert & Giulio Peruginelli. (2018) Adelic versions of the Weierstrass approximation theorem. Journal of Pure and Applied Algebra 222:3, pages 568-584.
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Xiumei Li & Min Sha. (2017) Gauss factorials of polynomials over finite fields. International Journal of Number Theory 13:08, pages 2039-2054.
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Jakub Byszewski, Mikołaj Fra̧czyk & Anna Szumowicz. (2017) Simultaneous p-orderings and minimizing volumes in number fields. Journal of Number Theory 173, pages 478-511.
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David Adam & Jean-Luc Chabert. (2015) On Bhargava's factorials of the set of twin primes in ℤ and in 𝔽 q [T] . International Journal of Number Theory 11:06, pages 1941-1959.
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Dinesh S. Thakur. (2015) Fermat versus Wilson congruences, arithmetic derivatives and zeta values. Finite Fields and Their Applications 32, pages 192-206.
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Jean-Luc Chabert, Sabine Evrard & Youssef Fares. (2014) Mahler's polynomial approximation for odd and even p-adic functions. Journal of Number Theory 144, pages 379-407.
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Rudolf HanelStefan Thurner & Murray Gell-Mann. (2014) How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems. Proceedings of the National Academy of Sciences 111:19, pages 6905-6910.
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Dinesh S. Thakur. (2012) Binomial and factorial congruences for . Finite Fields and Their Applications 18:2, pages 271-282.
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Keith Johnson. (2011) Computing -removed -orderings and -orderings of order . Actes des rencontres du CIRM 2:2, pages 33-40.
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David Adam & Paul-Jean Cahen. (2011) Newton and Schinzel sequences in quadratic fields. Actes des rencontres du CIRM 2:2, pages 15-20.
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Jean-Luc Chabert. (2011) An overview of some recent developments on integer-valued polynomials: Answers and Questions. Actes des rencontres du CIRM 2:2, pages 3-14.
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Keith Johnson. (2009) Limits of characteristic sequences of integer-valued polynomials on homogeneous sets. Journal of Number Theory 129:12, pages 2933-2942.
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Keith Johnson. (2008) P-orderings of finite subsets of Dedekind domains. Journal of Algebraic Combinatorics 30:2, pages 233-253.
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Keith Johnson. (2008) The invariant subalgebra and anti-invariant submodule of K * K (p) . Journal of K-Theory 2:1, pages 123-145.
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David Adam. (2008) Pólya and Newtonian function fields. manuscripta mathematica 126:2, pages 231-246.
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Michael P. Knapp. (2009) On systems of diagonal forms. Journal of the Australian Mathematical Society 82:2, pages 221-236.
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