Strong versions of Kummer-type congruences for Genocchi numbers and polynomials and tangent coefficients

Mehmet Cenkci

Acta Mathematica Universitatis Ostraviensis (2005)

  • Volume: 13, Issue: 1, page 3-11
  • ISSN: 1804-1388

Abstract

top
We use the properties of p -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.

How to cite

top

Cenkci, Mehmet. "Strong versions of Kummer-type congruences for Genocchi numbers and polynomials and tangent coefficients." Acta Mathematica Universitatis Ostraviensis 13.1 (2005): 3-11. <http://eudml.org/doc/35147>.

@article{Cenkci2005,
abstract = {We use the properties of $p$-adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.},
author = {Cenkci, Mehmet},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {$p$-adic integral; $p$-adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences; -adic integral; -adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences},
language = {eng},
number = {1},
pages = {3-11},
publisher = {University of Ostrava},
title = {Strong versions of Kummer-type congruences for Genocchi numbers and polynomials and tangent coefficients},
url = {http://eudml.org/doc/35147},
volume = {13},
year = {2005},
}

TY - JOUR
AU - Cenkci, Mehmet
TI - Strong versions of Kummer-type congruences for Genocchi numbers and polynomials and tangent coefficients
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2005
PB - University of Ostrava
VL - 13
IS - 1
SP - 3
EP - 11
AB - We use the properties of $p$-adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
LA - eng
KW - $p$-adic integral; $p$-adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences; -adic integral; -adic measures; Bernoulli numbers; Genocchi numbers; Genocchi polynomials; tangent coefficients; Kummer congruences
UR - http://eudml.org/doc/35147
ER -

References

top
  1. Carlitz L., 10.2307/2372625, , Amer. J. Math. 75 (1953) 163-172. (1953) Zbl0050.26703MR0051871DOI10.2307/2372625
  2. Carlitz L., 10.2307/2688488, , Math. Mag. 34 (1961) 131-146. (1961) Zbl0122.04702MR0130397DOI10.2307/2688488
  3. Carlitz L., Degenerate Stirling, Bernoulli and Eulerian numbers, , Utilitas Math. 15 (1979) 51-88. (1979) Zbl0404.05004MR0531621
  4. Comtet L., “Advanced Combinatorics. The Art of Finite and Infinite Expansions”, , Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. (1974) Zbl0283.05001MR0460128
  5. Dumont D., Interprètations combinatories des nombres de Genocchi, , Duke Math. J. 41 (1974) 305-318. (1974) MR0337643
  6. Dumont D. G. Vinnot, 10.1016/S0167-5060(08)70696-4, , Ann. Discrete Math. 6 (1980) 77-87. (1980) MR0593524DOI10.1016/S0167-5060(08)70696-4
  7. Dumont D. A. Randrianarivony, 10.1016/0012-365X(94)90230-5, , Discrete Math. 132 (1994) 37-49. (1994) MR1297370DOI10.1016/0012-365X(94)90230-5
  8. Dwork B., “Lectures on p -Adic Differential Equations”, , Springer-Verlag, New York, 1982. (1982) Zbl0502.12021MR0678093
  9. Fox G. J., 10.5802/jtnb.353, , J. Thèor. Nombres de Bordeaux 14 (2000) 187-204. Zbl1022.11008MR1925997DOI10.5802/jtnb.353
  10. Howard F. T., 10.1006/jnth.1995.1062, , J. Number Theory 52 (1995) 157-172. (1995) MR1331772DOI10.1006/jnth.1995.1062
  11. Jang L., Kim T., Park D.-W., 10.1016/S0096-3003(03)00314-X, , App. Math. Comput. 151 (2004) 589-593. MR2044223DOI10.1016/S0096-3003(03)00314-X
  12. Yang Y., Kim D. S., 10.1016/S0096-3003(02)00138-8, , App. Math. Comput. 137 (2003) 387-398. MR1950105DOI10.1016/S0096-3003(02)00138-8
  13. Nörlund N., “Vorlesungen Über Differenzenrechnung”, , Chelsea, New York, 1954. (1954) 
  14. Ramanujan S., “Collected Papers”, , Chelsea, New York, 1962. (1962) MR2280844
  15. Tsumura H., 10.3836/tjm/1270134514, , Tokyo J. Math. 10 (1987) 281-293. (1987) MR0926243DOI10.3836/tjm/1270134514
  16. Washington L., “Introduction to Cyclotomic Fields”, Springer-Verlag, , New York, 1982. (1982) MR0718674
  17. Young P. T., 10.1006/jnth.1999.2401, , J. Number Theory 78 (1999) 204-227. (1999) Zbl0939.11014MR1713481DOI10.1006/jnth.1999.2401
  18. Young P. T., 10.4064/aa99-3-5, , Acta Arith. 99 (2001) 277-288. Zbl0982.11008MR1845351DOI10.4064/aa99-3-5
  19. Young P. T., 10.1016/S0012-365X(02)00839-7, , Discrete Math. 270 (2003) 279-289. Zbl1042.11015MR1997904DOI10.1016/S0012-365X(02)00839-7
  20. Young P. T., 10.1016/j.disc.2004.03.011, , Discrete Math. 285 (2004) 289-296. Zbl1046.11011MR2062851DOI10.1016/j.disc.2004.03.011

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.