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On the joint 2-adic complexity of binary multisequences

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences with given joint 2-adic complexity.

On the joint 2-adic complexity of binary multisequences∗

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications

Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences...

On the k -polygonal numbers and the mean value of Dedekind sums

Jing Guo, Xiaoxue Li (2016)

Czechoslovak Mathematical Journal

For any positive integer k 3 , it is easy to prove that the k -polygonal numbers are a n ( k ) = ( 2 n + n ( n - 1 ) ( k - 2 ) ) / 2 . The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet L -functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums S ( a n ( k ) a ¯ m ( k ) , p ) for k -polygonal numbers with 1 m , n p - 1 , and give an interesting computational formula for it.

On the K-theory of the C * -algebra generated by the left regular representation of an Ore semigroup

Joachim Cuntz, Siegfried Echterhoff, Xin Li (2015)

Journal of the European Mathematical Society

We compute the K -theory of C * -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the K -theory of these semigroup C * -algebras in terms of the K -theory for the reduced group C * -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

On the L 1 norm of exponential sums

S. K. Pichorides (1980)

Annales de l'institut Fourier

The L 1 norm of a trigonometric polynomial with N non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of C ( log N ) / ( log log N ) 2 .

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