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On the cardinality of twelfth degree polynomial


Lasaraiya, Suriana and Sapar, Siti Hasana and Mohamat Johari, Mohamat Aidil (2016) On the cardinality of twelfth degree polynomial. In: 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016), 26-28 Jan. 2016, Kuala Lumpur, Malaysia. (pp. 1-9).


Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums associated with f modulo a prime pα is S(f:q)=∑e2πif(x)q for α>1, where f (x) is in Z[x] and the sum is taken over a complete set of residues x modulo positive integer q. Previous studies has shown that estimation of S (f; pα) is depends on the cardinality of the set of solutions to congruence equation associated with the polynomial. In order to estimate the cardinality, we need to have the value of p-adic sizes of common zeros of partial derivative polynomials associated with polynomial. Hence, p-adic method and newton polyhedron technique will be applied to this approach. After that, indicator diagram will be constructed and analyzed. The cardinality will in turn be used to estimate the exponential sums of the polynomials. This paper concentrates on the cardinality of the set of solutions to congruence equation associated with polynomial in the form of f (x, y) = ax12 + bx11y + cx10y2 + sx + ty + k.

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Official URL or Download Paper: http://aip.scitation.org/doi/abs/10.1063/1.4952488

Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1063/1.4952488
Publisher: AIP Publishing
Keywords: Cardinality; Polynomial
Depositing User: Nabilah Mustapa
Date Deposited: 08 Sep 2017 05:30
Last Modified: 08 Sep 2017 05:30
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4952488
URI: http://psasir.upm.edu.my/id/eprint/57171
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