J. Knopfmacher, Analytic arithmetic of algebraic function elds, Lecture Notes in Pure and Applied Mathematics, volume 50, Marcel Dekker, Inc., New York and Basel, 1979. Home/Search Document Not in Database Summary Related Articles Check |
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Asymptotic Behaviour of Some Infinite Products Involving Prime.. - Hwang (1996) (Correct)
....(cf. 13, p. 239] the methods developed here have wide applications to other entire functions de ned via in nite products issuing from arithmetical functions or combinatorial structures: integers subject to arithmetical constraints (cf. 14] arithmetical semigroups under Axiom A # (cf. [11, 12, 5]) the combinatorial schemes of Flajolet and Soria (cf. 5] 8, Ch. 5] factorisatio numerorum in arithmetical semigroups (cf. 10] and the combinatorial scheme developed by the author (having an exponential singularity) cf. 8, Chs. 6,9] etc. Of these, an interesting example is the random ....
J. Knopfmacher, Analytic arithmetic of algebraic function elds, Lecture Notes in Pure and Applied Mathematics, volume 50, Marcel Dekker, Inc., New York and Basel, 1979.
A Poisson * geometric convolution law for the number of components .. - Hwang (1995) (Correct)
....is negligible comparing with I 7 . Lemma 9 For m 1 and n m 1, we have Proof. Omitted. Collecting the results of the lemmas in this section completes the proof of Theorem 6. 19 5 Applications In this section, we indicate some applications of our theorems. For further examples, see [11, 24, 25]. Example 1. Random mapping patterns. By random mapping [26] we mean a random singled valued mapping of the set f1; 2; 3; ng into itself. These structures have been extensively studied in the literature due both to their intrinsic interest and their wide applications to many di erent ....
J. Knopfmacher. Analytic arithmetic of algebraic function elds, Lecture Notes in Pure and Applied Mathematics, volume 50. Marcel Dekker, Inc., New York and Basel, 1979.
John Knopfmacher and additive arithmetical semigroups - Warlimont Self-citation (Knopfmacher) (Correct)
....results which I achieved were rewarded immediately: Already in October 1989 John invited me to Wits. February, March, April 1991 which I spent there also mark the beginning of my love a air with South Africa. Additive arithmetical semigroups are structures which have been created and pioneered in [2] by John. We quote the system of axioms. Let G be a commutative semigroup ( denotes the group operation) with neutral element e which contains a non empty subset P of elements p 6= e such that any element 6= e of G can be written as a product of elements of P in one and but for the arrangement ....
....(1) a b) a) b) for all a; b; 2 G, 2) fa 2 Gj (a) ng is nite for all n 2 IN o . Then G together with is an additive arithmetical semigroup . In view of the deceptively simple axiomatic structute one would hardly expect the beauty and wealth of the theory. John s monograph [2] has in its rst chapter a list of examples. They all satisfy a condition called axiom A : there are constants A 0; q 1; 0 1) such that (n) #fa Gj (a) ng = Aq n ) as n 1: The Zeta function Z(z) associated with (G; is the power series Z(z) n=0 (n)z whose ....
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John Knopfmacher. Analytic Arithmetic of Algebraic Function eld. Lecture Notes. Marcel Dekker 1979. Author's address The John Knopfmacher Centre for Applicable Analysis and Number Theory
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