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An Estimating the p-adic Sizes of Common Zeros of Partial Derivative Polynomials

Year 2013, Volume: 1 Issue: 1, 38 - 48, 01.04.2013

Siti Hasana Sapar Kamel Ariffin Mohd Atan Siti Syaheera Aminuddin

Abstract

Let be a vector in the space with ring of integers and be a positive integer, a polynomial in with coefficient in . The exponential sum associated with is defined as a complete set of residues modulo . The value of depend on the estimate of cardinality , the number of elements , where the sum is taken over

Keywords

Exponential sums cardinality; p-adic sizes; Newton polyhedron

References

  • Chan, K. L. and Mohd. Atan, K. A. 1997. On the Estimate to Solutions of Congruence Equations Associated with a Quartic Form, J. Phys. Sci. 8: 21-34.
  • Heng, S. H. and Mohd. Atan, K. A. 1999. An Estimation of Exponential Sums Associated with a Cubic Form, J. Phys. Sci. 10: 1-21.
  • Loxton, J. H. and Smith, R. A. 1982. Estimate for Multiple Exponential Sums, J. Aust. Math. Soc. 33: 125-134.
  • Loxton, J. H. and Vaughan, R. C. 1985. The Estimate of Complete Exponential Sums, Canad. Math. Bull. 28(4): 440-454.
  • Mohd. Atan, K. A. 1986. Newton polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in , Pertanika 9(3): 375-380.
  • Mohd. Atan, K. A. and Loxton, J. H. Newton polyhedra and solutions of congruences, In Proceeding of Diophantine Analysis, Cambridge University Press, 1986, eds. Loxton, J. H. and Poorten, A. Van der. pp. 67-82, 1986.
  • Sapar, S. H. and Mohd. Atan, K. A. 2002. Estimate for the Cardinality of the Set of Solution to Congruence Equations, J. Technology 36(C): 13
  • Sapar, S. H. and Mohd. Atan, K. A. 2009. A Method of Estimating the p-adic Sizes of Common Zeros of Partial Derivative Polynomials
  • Associated with a Quintic Form, World Scientific 5: 541-554. Yap, H. K., Sapar, S. H. and Mohd. Atan, K. A. 2011. Estimation of p-adic Sizes of Common Zeros of Partial Derivative Associated with a
  • Cubic Form, Sains Malaysiana 40(8): 921-926.

Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang

Year 2013, Volume: 1 Issue: 1, 38 - 48, 01.04.2013

Siti Hasana Sapar Kamel Ariffin Mohd Atan Siti Syaheera Aminuddin

Abstract

References

  • Chan, K. L. and Mohd. Atan, K. A. 1997. On the Estimate to Solutions of Congruence Equations Associated with a Quartic Form, J. Phys. Sci. 8: 21-34.
  • Heng, S. H. and Mohd. Atan, K. A. 1999. An Estimation of Exponential Sums Associated with a Cubic Form, J. Phys. Sci. 10: 1-21.
  • Loxton, J. H. and Smith, R. A. 1982. Estimate for Multiple Exponential Sums, J. Aust. Math. Soc. 33: 125-134.
  • Loxton, J. H. and Vaughan, R. C. 1985. The Estimate of Complete Exponential Sums, Canad. Math. Bull. 28(4): 440-454.
  • Mohd. Atan, K. A. 1986. Newton polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in , Pertanika 9(3): 375-380.
  • Mohd. Atan, K. A. and Loxton, J. H. Newton polyhedra and solutions of congruences, In Proceeding of Diophantine Analysis, Cambridge University Press, 1986, eds. Loxton, J. H. and Poorten, A. Van der. pp. 67-82, 1986.
  • Sapar, S. H. and Mohd. Atan, K. A. 2002. Estimate for the Cardinality of the Set of Solution to Congruence Equations, J. Technology 36(C): 13
  • Sapar, S. H. and Mohd. Atan, K. A. 2009. A Method of Estimating the p-adic Sizes of Common Zeros of Partial Derivative Polynomials
  • Associated with a Quintic Form, World Scientific 5: 541-554. Yap, H. K., Sapar, S. H. and Mohd. Atan, K. A. 2011. Estimation of p-adic Sizes of Common Zeros of Partial Derivative Associated with a
  • Cubic Form, Sains Malaysiana 40(8): 921-926.
There are 10 citations in total.

Details

Authors

Siti Hasana Sapar This is me

Kamel Ariffin Mohd Atan This is me

Siti Syaheera Aminuddin This is me

Publication Date April 1, 2013
Published in Issue Year 2013 Volume: 1 Issue: 1

Cite

APA Sapar, S. H., Atan, K. A. M., & Aminuddin, S. S. (2013). Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang. New Trends in Mathematical Sciences, 1(1), 38-48.
AMA Sapar SH, Atan KAM, Aminuddin SS. Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang. New Trends in Mathematical Sciences. April 2013;1(1):38-48.
Chicago Sapar, Siti Hasana, Kamel Ariffin Mohd Atan, and Siti Syaheera Aminuddin. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences 1, no. 1 (April 2013): 38-48.
EndNote Sapar SH, Atan KAM, Aminuddin SS (April 1, 2013) Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang. New Trends in Mathematical Sciences 1 1 38–48.
IEEE S. H. Sapar, K. A. M. Atan, and S. S. Aminuddin, “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”, New Trends in Mathematical Sciences, vol. 1, no. 1, pp. 38–48, 2013.
ISNAD Sapar, Siti Hasana et al. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences 1/1 (April2013), 38-48.
JAMA Sapar SH, Atan KAM, Aminuddin SS. Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang. New Trends in Mathematical Sciences. 2013;1:38–48.
MLA Sapar, Siti Hasana et al. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences, vol. 1, no. 1, 2013, pp. 38-48.
Vancouver Sapar SH, Atan KAM, Aminuddin SS. Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang. New Trends in Mathematical Sciences. 2013;1(1):38-4.