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Abstract
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 padic sizes of common zeros of partial derivative polynomials associated with polynomial. Hence, padic 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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