Moments of additive functions and sieve methods

1984 ◽  
pp. 1-25
Author(s):  
Krishnaswami Alladi
Keyword(s):  
Additive Functions ◽  
Sieve Methods

Results of Linear Cryptanalysis Using Linear Sieve Methods

2009 ◽  
Vol E92-A (5) ◽  
pp. 1347-1355
Author(s):  
Yukiyasu TSUNOO ◽  
Hiroki NAKASHIMA ◽  
Hiroyasu KUBO ◽  
Teruo SAITO ◽  
Takeshi KAWABATA
Keyword(s):  
Linear Cryptanalysis ◽  
Sieve Methods

scholarly journals On $p$ and $q$-Additive Functions

1999 ◽  
Vol 22 (1) ◽  
pp. 83-97 ◽  
Author(s):  
Yoshihisa UCHIDA
Keyword(s):  
Additive Functions

scholarly journals A Lebesgue decomposition for elements in a topological group

1980 ◽  
Vol 3 (4) ◽  
pp. 801-808
Author(s):  
Thomas P. Dence
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Projection Operators ◽  
Additive Functions ◽  
Lebesgue Decomposition ◽  
Algebra Of Sets

Our aim is to establish the Lebesgue decomposition for strongly-bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly-bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly-bounded additive functions defined on an algebra of sets. Analagous results follow for lattices of sets. Generalizing some of the techniques yield decompositions for elements in a topological group.

scholarly journals The normality of digits in almost constant additive functions

2012 ◽  
Vol 171 (3-4) ◽  
pp. 481-497 ◽  
Author(s):  
J. Vandehey
Keyword(s):  
Additive Functions

The paucity problem for simultaneous quadratic and biquadratic equations

1999 ◽  
Vol 126 (2) ◽  
pp. 209-221 ◽  
Author(s):  
W. Y. TSUI ◽  
T. D. WOOLEY
Keyword(s):  
Lower Bounds ◽  
Diophantine Equations ◽  
Upper And Lower Bounds ◽  
Current Interest ◽  
Sieve Methods ◽  
Number Of Solutions ◽  
Simultaneous Diophantine Equations ◽  
History Of

The problem of constructing non-diagonal solutions to systems of symmetric diagonal equations has attracted intense investigation for centuries (see [5, 6] for a history of such problems) and remains a topic of current interest (see, for example, [2–4]). In contrast, the problem of bounding the number of such non-diagonal solutions has commanded attention only comparatively recently, the first non-trivial estimates having been obtained around thirty years ago through the sieve methods applied by Hooley [10, 11] and Greaves [7] in their investigations concerning sums of two kth powers. As a further contribution to the problem of establishing the paucity of non-diagonal solutions in certain systems of diagonal diophantine equations, in this paper we bound the number of non-diagonal solutions of a system of simultaneous quadratic and biquadratic equations. Let S(P) denote the number of solutions of the simultaneous diophantine equationsformula herewith 0[les ]xi, yi[les ]P(1[les ]i[les ]3), and let T(P) denote the corresponding number of solutions with (x1, x2, x3) a permutation of (y1, y2, y3). In Section 4 below we establish the upper and lower bounds for S(P)−T(P) contained in the following theorem.

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