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

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

Siti Hasana Sapar Kamel Ariffin Mohd Atan Siti Syaheera Aminuddin

https://izlik.org/JA43GY63NN

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

Anahtar Kelimeler

Exponential sums , cardinality; p-adic sizes; Newton polyhedron

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

https://izlik.org/JA43GY63NN

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.