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Some Questions about Counting Functions of Finite Abelian Groups

Author: GaoShuZuo
Tutor: DiWenGuang
School: Shandong Normal University
Course: Basic mathematics
Keywords: Euler product The residue theorem Perron formula The problem of inter-cell
CLC: O152.1
Type: Master's thesis
Year: 2011
Downloads: 12
Quote: 1
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Abstract


Let a (n) represents the number of all non-isomorphic Abelian group known every prime number p, the number of natural alpha ≥ 1 s ( pα ) = P ( alpha ) , where P ( a ) said alpha unconstrained divided number of particularly we have a ( 1 ) = 1 , a ( p ) = 1 , a ( p2 ) = 2, a ( p3 ) = 3 , a ( P4 ) = 5 a ( P5 ) = 7 , a ( p6 ) = 11 , a ( p7 ) = 15 ( 1 ) the number of finite Abelian group function n ( n ) the mean number theory have to do in-depth research : P.Erdos, G.Szekeres first prove Kendall , of Rankin card H. - E.Richert card was made ??following the recent research : △ ( x ) \(x) \; △ ( x ) \the n = p1α1 ... psαs if αj ≥ k (j = 1, ..., s), which means that the characteristic function of the k - full number , then n is called the k - full number . ORDER δk ( n ) we have the following two theorems : Theorem 1 we have the asymptotic formula where Pj ( t ) ( j = 1,2 ) t j -order polynomials . Theorem 2 we have asymptotic formula where Qj ( t ) ( j = 2,4,6 ) t j-th polynomial . below we prove that a hypothetical result : Theorem 3 Riemann zeta function Lindelof hypothesis holds , where Hp ( j ) -1 ( t ) t -1 polynomial P ( j ) .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Finite group theory
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