1 9 N ov 2 00 4 Power Sums Related to Semigroups S ( d 1 , d 2 , d 3 )

Power Sums Related to Semigroups S ( d 1 , d 2 , d 3 ) Leonid

The explicit formulas for the sums of positive powers of the integers s i unrepresentable by the triple of integers d 1 , d 2 , d 3 ∈ N, gcd(d 1 , d 2 , d 3) = 1, are derived. For short we denote the tuple (d 1 ,. .. , d m) by d m and consider the generating function Φ (d m ; z)

On the Graphs Related to Green Relations of Finite Semigroups

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

N ov 2 00 4 THE NUMBER OF S 4 FIELDS WITH GIVEN DISCRIMINANT

We prove that the number of S 4-extensions of the rationals of given discriminant d is O(d 1/2+ǫ) for all ǫ > 0. For a prime number C we derive that the number of octahedral modular forms of weight 1 and conductor C is bounded above by O(C 1/2 log(C) 2).

N ov 2 00 3 BOTTOM SCHUR FUNCTIONS

We give a basis for the space spanned by the sumˆs λ of the lowest degree terms in the expansion of the Schur symmetric functions s λ in terms of the power sum symmetric functions p µ , where deg(p i) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned byˆs λ , where λ is a partition of n, is equal to the number of partitions of n ...

ar X iv : h ep - t h / 05 11 16 1 v 2 1 9 N ov 2 00 6 The Effective Potential in the Massive φ 4 4 Model