On properties of the Weil sums over finite fields and finite Abelian groups

1999 ◽  
Vol 9 (3) ◽  
Author(s):  
O. A. LOGACHEV ◽  
A. A. SALNIKOV ◽  
V. V. YASHCHENKO
Keyword(s):  
Finite Fields ◽  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Weil Sums

scholarly journals Counting Compositions over Finite Abelian Groups

10.37236/7591 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Zhicheng Gao ◽  
Andrew MacFie ◽  
Qiang Wang
Keyword(s):  
Transfer Matrix ◽  
Finite Fields ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Abelian Groups ◽  
Type I ◽  
Type Ii ◽  
Finite Abelian Groups ◽  
Frobenius Theorem ◽  
Exact Counting

We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields can be converted to type (i) compositions, whereas Carlitz and "locally Mullen" compositions can be formulated as type (ii) compositions. We use the multisection formula to translate the problem from integers to group elements, the transfer matrix method to do exact counting, and finally the Perron-Frobenius theorem to derive asymptotics. We also exhibit bijections involving certain restricted classes of compositions.

scholarly journals On efficient computation of sums of characters on the basis of A. G. Postnikov methods

2021 ◽  
pp. 13-16
Author(s):  
Nikolaj Glazunov
Keyword(s):  
Finite Fields ◽  
Prime Power ◽  
Abelian Groups ◽  
Summation Method ◽  
Kloosterman Sums ◽  
Efficient Computation ◽  
Finite Abelian Groups

An efficient p-adic method and the structure of an algorithm for computing the sums of characters of finite abelian groups are presented. The method and algorithm are based on the A.G. Postnikov summation method of characters modulo a prime power and its developments. A brief survey of the theory of characters of finite abelian groups, p-adic arithmetic and analysis is presented. Questions of the efficiency of p-adic methods are discussed. Moreover, we present results of computation of other types of sums of characters (Kloosterman sums), which are connecting with Artin-Schreier coverings over prime finite fields. The corresponding method and algorithm are based on the development of another method by A.G. Postnikov. Examples of computation of sums of characters are given.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Sum-free subsets of finite abelian groups of type III

2016 ◽  
Vol 58 ◽  
pp. 181-202 ◽  
Author(s):  
R. Balasubramanian ◽  
Gyan Prakash ◽  
D.S. Ramana
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Type Iii
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