Character sums and products of factorials modulo p

Moubariz Z. Garaev[1]; Florian Luca[2]

  • [1] Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58180, Morelia, Michoacán, México
  • [2] Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58180, Morelia, Michoacán, México

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 151-160
  • ISSN: 1246-7405

Abstract

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In this paper, we apply character sum estimates to study products of factorials modulo p .

How to cite

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Garaev, Moubariz Z., and Luca, Florian. "Character sums and products of factorials modulo $p$." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 151-160. <http://eudml.org/doc/249451>.

@article{Garaev2005,
abstract = {In this paper, we apply character sum estimates to study products of factorials modulo $p$.},
affiliation = {Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58180, Morelia, Michoacán, México; Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58180, Morelia, Michoacán, México},
author = {Garaev, Moubariz Z., Luca, Florian},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {congruences; number of solutions},
language = {eng},
number = {1},
pages = {151-160},
publisher = {Université Bordeaux 1},
title = {Character sums and products of factorials modulo $p$},
url = {http://eudml.org/doc/249451},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Garaev, Moubariz Z.
AU - Luca, Florian
TI - Character sums and products of factorials modulo $p$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 151
EP - 160
AB - In this paper, we apply character sum estimates to study products of factorials modulo $p$.
LA - eng
KW - congruences; number of solutions
UR - http://eudml.org/doc/249451
ER -

References

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  1. W. Banks, F. Luca, I. E. Shparlinski, H. Stichtenoth, On the value set of n ! modulo a prime. Turkish J. Math. 29 no. 2 (2005), 169–174. Zbl1161.11386MR2142292
  2. D. A. Burgess, On character sums and L -series, II. Proc. London Math. Soc. (3) 13 (1963), 524–536. Zbl0123.04404MR148626
  3. M. Z. Garaev, F. Luca, I. E. Shparlinski, Character sums and congruences with n ! . Trans. Amer. Math. Soc. 356 (2004), 5089–5102. Zbl1060.11046MR2084412
  4. M. Z. Garaev, F. Luca, I. E. Shparlinski, Exponential sums and congruences with factorials. J. reine angew. Math., to appear. Zbl1071.11051MR2155084
  5. M. Z. Garaev, F. Luca, I. E. Shparlinski, Waring problem with factorials mod p . Bull. Australian Math. Soc. 71 (2005), 259–264. Zbl1076.11013MR2133409
  6. A. A. Karatsuba, The distribution of products of shifted prime numbers in arithmetic progressions. Dokl. Akad. Nauk SSSR 192 (1970), 724–727 (in Russian). Zbl0224.10043MR269611
  7. F. Luca, P. Stănică, Products of factorials modulo p . Colloq. Math. 96 no. 2 (2003), 191–205. Zbl1042.11002MR2010354
  8. A. Sárkőzy, On the distribution of residues of products of integers. Acta Math. Hung. 49 (3-4) (1987), 397–401. Zbl0629.10004MR891052

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