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Computer Algebra , Malaga, p. 135 – 139 ( 2013 ). [12] Margulis , G. , Explicit group-theoretical constructions of combinatorial schemes and their application to

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–New York–Oxford, 1988 . [12] Tamura , J. , Explicit formulae for Cantor series representing quadratic irrationals , Number Theory

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Periodica Mathematica Hungarica
Authors: Pakwan Riyapan, Vichian Laohakosol, and Tuangrat Chaichana

Summary  

Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method. The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization. Similar results are also established for continued fractions in the field of formal series over a finite base field.

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Abstract

For integers m, n, q, k, with q,k≧1 and Dirichlet characters we define a generalized Kloosterman sum
ea
with a Dirichlet character and a Gauss sum G(a,χ′) as coefficient, where e(z)=e 2πiz. The aim of this paper is to study the fourth power mean
eb
obtaining explicit formulas for M k(q).
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We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non disjoint support. This extends the work of Costello and Lauter in [12] who calculated explicit formulæ for divisor doubling and addition of divisors with disjoint support in JF(C) using only base field operations. Explicit formulæ is presented for this third case and a different approach for divisor doubling.

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.001 Discussion The paper is the first to my knowledge to explicitly examine the relationship between an invention's usefulness and the socioculturally oriented relatedness of its features. Generally speaking, a statistically significant inverse U

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Abstract  

We shall investigate several properties of the integral

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int_1^\infty {t^{ - \theta } \Delta _k \left( t \right) log^j t dt}$$ \end{document}
with a natural number k, a non-negative integer j and a complex variable θ, where Δk(x) is the error term in the divisor problem of Dirichlet and Piltz. The main purpose of this paper is to apply the “elementary methods” and the “elementary formulas” to derive convergence properties and explicit representations of this integral with respect to θ for k = 2.

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