The quotients Gk/Gk+1 of the lower central series of a finitely presented group G are an important invariant of this group. In this work we investigate the ranks of these quotients in the case of a certain class of conjugation-free groups, which are groups generated by x1, . . . , xn and having only cyclic relations: xitxit−1 · . . . · xi1 = xit−1 · . . . · xi1xit = · · · = xi1xit · . . . · xi2...

The well-known Birch and Swinnerton-Dyer conjecture gives a deep connection between the leading coefficient of the L-series and the arithmetic properties of an abelian variety. Both are very important and subtle. This paper is part of an effort to compute the analytic side explicitly in a special case. Indeed, we are interested in the central derivative of certain algebraic Hecke L-series, rela...

Doctor Musana is a general internal medicine resident and Doctor Yale is a general internal medicine physician with Marshfield Clinic, and Marshfield Clinic Research Foundation, Marshfield, Wis. Please address correspondence to: Steven H Yale, MD, General Internal Medicine, Marshfield Clinic, 1000 N Oak Ave, Marshfield, WI 54449; phone 715.387.9110; fax 715.389.3808; e-mail yale.steven@mcrf. mf...

The notion of central series for groups with action on itself is introduced. An analogue of Witt’s construction is given for such groups. A certain condition is found for the action and the corresponding category is defined. It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restri...

In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals generated by the elements Li. We give a complete description of the structure of these quotients for the free metabelian associative algebra A/(A[A,A][A,A]). With methods from Polynomial Identities the...

We prove, in standard notation from spectral theory, the asymptotic formula (B > 0) ∑ κj≤T αjHj( 1 2 ) = ( T π ) 2 − BT log T +O(T (log T )), by using an approximate functional equation for Hj( 1 2 ) and the Bruggeman-Kuznetsov trace formula. We indicate how the error termmay be improved to O(T (log T )ε).

(T ε ≤ K ≤ T ) are considered, where αj = |ρj(1)| (coshπκj) , and ρj(1) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λj = κ 2 j + 1 4 to which the Hecke series Hj(s) is attached. The problem is transformed to the estimation of a classical exponential sum involving the binary additive divisor problem. The analogous exponential sums with Hj( 1 2 ) or H j...

INTRODUCTION Paracoccidioidomycosis (PCM) is the most important systemic mycosis in South America. Central nervous system involvement is potentially fatal and can occur in 12.5% of cases. This paper aims to contribute to the literature describing eight cases of neuroparacoccidioidomycosis (NPMC) and compare their characteristics with patients without neurological involvement, to identify unique...

The Central Sudanic [CSD] languages are spoken in central Africa over parts of the D.R.C., Uganda, Sudan, C.A.R. and Chad. They comprise six subgroups of unequal size (representative languages are indicated in parentheses): – [MMD] Moru-Madi (Moru, Avokaya, Logo, Lugbara, Ma’di), – [LND] Lendu (Ngiti, Lendu), – [MAS] Mangbetu(-Asua) (Asua, Mangbetu, Meje, Lombi), – [MEF] Mangbutu-Efe (Mangbutu,...