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

Yıl 2013, Cilt: 1 Sayı: 1, 38 - 48, 01.04.2013

Öz

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

Kaynakça

  • 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

Yıl 2013, Cilt: 1 Sayı: 1, 38 - 48, 01.04.2013

Öz

Kaynakça

  • 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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Siti Hasana Sapar Bu kişi benim

Kamel Ariffin Mohd Atan Bu kişi benim

Siti Syaheera Aminuddin Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 1 Sayı: 1

Kaynak Göster

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. Nisan 2013;1(1):38-48.
Chicago Sapar, Siti Hasana, Kamel Ariffin Mohd Atan, ve Siti Syaheera Aminuddin. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences 1, sy. 1 (Nisan 2013): 38-48.
EndNote Sapar SH, Atan KAM, Aminuddin SS (01 Nisan 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, ve S. S. Aminuddin, “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”, New Trends in Mathematical Sciences, c. 1, sy. 1, ss. 38–48, 2013.
ISNAD Sapar, Siti Hasana vd. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences 1/1 (Nisan 2013), 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 vd. “Department of Mathematics, Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang”. New Trends in Mathematical Sciences, c. 1, sy. 1, 2013, ss. 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.