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Correlations of multiplicative functions in function fields
Mathematika, 2022 AbstractWe develop an approach to study character sums, weighted by a multiplicative function , of the formwhere χ is a Dirichlet character and ξ is a short interval character over . We then deduce versions of the Matomäki–Radziwiłł theorem and Tao's two‐point logarithmic Elliott conjecture over function fields , whereqis fixed.
Klurman, Oleksiy +2 more
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Some characterizations of specially multiplicative functions
International Journal of Mathematics and Mathematical Sciences, 2003 A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n.
Pentti Haukkanen
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An equation involving the F.Smarandache multiplicative function [PDF]
, 2007 The main purpose of this paper is using the elementary methods to study the solutions of an equation involving the F.Smarandache multiplicative function, and give its all positive integer ...
Chen, Jianbin
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Solutions and Stability of Generalized Kannappan’s and Van Vleck’s Functional Equations
Annales Mathematicae Silesianae, 2018 We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations ∫Sf(xyt)dµ(t)+∫Sf(xσ(y)t)dµ(t)= 2f(x)f(y), x,y ∈ S; ∫Sf(xσ(y)t)dµ(t)-∫Sf(xyt)dµ(t)= 2f(x)f(y), x,y ∈ S; where S is a semigroup, σ is an involutive automorphism of S ...
Elqorachi Elhoucien, Redouani Ahmed
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Majorisation with applications to the calculus of variations [PDF]
, 2001 This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of ...
Baker +20 more
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WNTs: Multiple Genes, Multiple Functions [PDF]
Journal of Investigative Dermatology, 2003 The development of ectodermal appendages such as hair, feathers and teeth has long fascinated biologists, who have attempted to understand how cells of different types interact with each other to induce the coordinated changes in cell shape, proliferation, adhesion and movement required for the formation of these intricate three-dimensional structures.
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On the Complexity of Computing Two Nonlinearity Measures [PDF]
, 2014 We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time $2^{O(n)}$ given the ...
A.A. Razborov +10 more
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Some characterizations of totients
International Journal of Mathematics and Mathematical Sciences, 1996 An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient.
Pentti Haukkanen
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On Schur multiple zeta functions: A combinatoric generalization of multiple zeta functions [PDF]
Advances in Mathematics, 2018 We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence and the case where all variables are the same.
Nakasuji, M. +2 more
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Hermite–Hadamard type inequalities for multiplicatively harmonic convex functions
Journal of Inequalities and Applications, 2023 In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established.
Serap Özcan, Saad Ihsan Butt
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