Introduction to Analytic Number
                    Theory

Postnikov, A. G.

doi:10.1090/mmono/068

Cited by 81 publications

(55 citation statements)

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“…Later on, Heupel [26] and, finally, Kaufman [27] replaced the error term in Pail's formula by an asymptotic expansion (cf. [28,29]), thus obtaining a complete analogue of (12).…”

Section: B'(x;o)--(logxmentioning

confidence: 99%

Distribution of values of Fourier coefficients for modular forms of weight 1

Fomenko¹

1998

J Math Sci

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“…Later on, Heupel [26] and, finally, Kaufman [27] replaced the error term in Pail's formula by an asymptotic expansion (cf. [28,29]), thus obtaining a complete analogue of (12).…”

Section: B'(x;o)--(logxmentioning

confidence: 99%

Distribution of values of Fourier coefficients for modular forms of weight 1

Fomenko¹

1998

J Math Sci

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“…There is a well-developed theory with many general results about the existence of means of arithmetic functions, see Elliott (1985); Indlekofer (1980Indlekofer ( , 1981Postnikov (1988). However, those general results do not imply the specific statements of this work.…”

mentioning

confidence: 84%

Average order in cyclic groups

Gathen¹,

Knopfmacher²,

Luca³

et al. 2004

J. Théor. Nombres Bordeaux

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Résumé. Pour chaque entier naturel n, nous déterminons l'ordre moyen α(n) deséléments du groupe cyclique d'ordre n. Nous montrons que plus de la moitié de la contributionà α(n) provient des ϕ(n)éléments primitifs d'ordre n. Il est par conséquent intéressant d'étudierégalement la fonction β(n) = α(n)/ϕ(n). Nous détermi-nons le comportement moyen de α, β, 1/β et considérons aussi ces fonctions dans le cas du groupe multiplicatif d'un corps fini.Abstract. For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We determine the mean behavior of α, β, 1/β, and also consider these functions in the multiplicative groups of finite fields.

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“…Our starting point here is the following simple formula for g(e~z] as ζ -> 0 (see Section 2.7 in [14]), which is due to Freiman: uniformly within the corner {z\ 3(z) < ε91(ζ),91(ζ) > 0},ε > 0 being fixed. If we let in this formula χ = e~z, then χ -> 1 and…”

Section: Generating Functions and Preliminary Asymptoticsmentioning

confidence: 99%

“…To get the coefficient of -Θ 2 in the last exponent of (11), notice first that it follows from (6) and (7) that b(r n ) = (2/π)6'/ 2 η 3 / 2 (1 + Ο(λ/η 1 / 2 }) (14) Brought to you by | The University of Auckland Library Authenticated Download Date | 6/10/15 5:57 AM as n -t oo. Therefore 2r" \ n 2 r 2 , χ π 2 12(1-r") 2 V ' l-rj 6(l-r") 3 ' ^"' 6(1-r") 3…”

Section: Generating Functions and Preliminary Asymptoticsmentioning

confidence: 99%