• Corpus ID: 227745738

Derangements and the $p$-adic incomplete gamma function.

@article{ODesky2020DerangementsAT,
  title={Derangements and the \$p\$-adic incomplete gamma function.},
  author={Andrew O’Desky and D. Harry Richman},
  journal={arXiv: Number Theory},
  year={2020}
}
We introduce a new $p$-adic analogue of the incomplete gamma function. We also introduce a closely related family of combinatorial sequences counting derangements and arrangements in certain wreath products. 
1 Citations
On pseudo-polynomials divisible only by a sparse set of primes and $\a$-primary pseudo-polynomials
We explore two questions about pseudo-polynomials, which are functions f : N → Z such that k divides f(n+ k)− f(n) for all n, k. First, for certain arbitrarily sparse sets R, we construct

References

SHOWING 1-10 OF 32 REFERENCES
A p-adic analogue of the Γ-function
  • J. Fac. Sci. Univ. Tokyo Sect. IA Math., 22(2):255–266
  • 1975
Interpolation $p$-adique
© Bulletin de la S. M. F., 1964, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord
An Interpolation Series for Continuous Functions of a p-adic Variable.
The theory of analytic functions of a p-adic variable (i. e. of functions defined by power series) is much simpler than that of complex analytic funktions and offers few surprises. On the other band,
Analyse p-adique et suites classiques de nombres
Soit (an)n∈N une suite de nombres rationnels (ou plus généralement de nombres algébriques sur Q et soit p un nombre premier. On sait que la suite (an)n∈N est pour tout h ∈ N périodique modulo p à
Einige Sätze über Primzahlen mit Anwendungen auf Irreduzibilitätsfragen I
  • II. Sitzungsberichte Preuss. Akad. Wiss. Phys.-Math. Klasse, pages 125–136, 152–173
  • 1929
On pseudo-polynomials
In a recent paper [1] I made the following Definition. The function f: ℤ + ∪ {0} → ℤ is a pseudo-polynomial if for all integers n ≥ 0, k ≥ 1.
Equidistribution from the Chinese Remainder Theorem
We prove the equidistribution of subsets of $(\Rr/\Zz)^n$ defined by fractional parts of subsets of~$(\Zz/q\Zz)^n$ that are constructed using the Chinese Remainder Theorem.
Functions with integral divided differences
Let $s_0,s_1,s_2,\ldots$ be a sequence of integers whose $m$th divided difference is integer-valued. We prove that $s_n$ is given by a polynomial in $n$ if there exists a positive number $\theta$
Functions with integral divided differences, 2020
  • DERANGEMENTS AND THE P -ADIC INCOMPLETE GAMMA FUNCTION
  • 2020
Identities behind some congruences for r-Bell and derangement polynomials
We derive new congruences bounding r-Bell and derangement polynomials, which generalize the existing ones, while the presented approach is significantly simpler and, at the same time, more
...
1
2
3
4
...