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pro vyhledávání: '"Ahmed, Md. Helal"'
In this paper, we present the fast computational algorithms for the Jacobi sums of orders $l^2$ and $2l^{2}$ with odd prime $l$ by formulating them in terms of the minimum number of cyclotomic numbers of the corresponding orders. We also implement tw
Externí odkaz:
http://arxiv.org/abs/1908.04263
Autor:
Ahmed, Md. Helal, Tanti, Jagmohan
The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing results co
Externí odkaz:
http://arxiv.org/abs/1906.09960
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the formulati
Externí odkaz:
http://arxiv.org/abs/1906.06921
Autor:
Ahmed, Md Helal, Tanti, Jagmohan
Publikováno v:
Bulletin of Pure and Applied Sciences (2019)
Jacobi sums and cyclotomic numbers are the important objects in number theory. The determination of all the Jacobi sums and cyclotomic numbers of order $e$ are merely intricate to compute. This paper presents the lesser numbers of Jacobi sums and cyc
Externí odkaz:
http://arxiv.org/abs/1906.07657
Autor:
Ahmed, Md Helal, Tanti, Jagmohan
The congruences for Jacobi sums of some lower orders has been treated by many authors in the literature. In this paper we establish the congruences for Jacobi sums of order 2l^2 with odd prime l. These congruences are useful to obtain algebraic and a
Externí odkaz:
http://arxiv.org/abs/1902.10512
The problem of determining cyclotomic numbers in terms of the solutions of certain Diophantine systems has been treated by many authors since the age of Gauss. In this paper we obtain an explicit expression for cyclotomic numbers of order 2l^2 in ter
Externí odkaz:
http://arxiv.org/abs/1807.07708
Autor:
Ahmed, Md. Helal, Tanti, Jagmohan
The aim of this paper is to deal with congruences for Jacobi sums of order $2l^{2}$ over a finite field $\mathbb{F}_{q}, q=p^{r}$, $p^{r}\equiv 1\ (mod \ 2l^{2})$, where $l>3$ and $p$ are primes. Further, we also calculate Jacobi sums $J_{2l^{2}}(1,n
Externí odkaz:
http://arxiv.org/abs/1807.06218
Publikováno v:
Indian Journal of Pure & Applied Mathematics; Jun2023, Vol. 54 Issue 2, p330-343, 14p
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