We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4, Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computatio...

The purpose of this paper is to justify the claim that a method for generating primes presented at EUROCRYPT'89 generates primes with virtually uniform distribution. Using convincing heuristic arguments, the conditional probability distributions of the size of the largest prime factor p 1 (n) of a number n on the order of N is derived, given that n satisses one of the conditions 2n+1 is prime, ...

We present a new algorithm that nds all primes up to n using at most O(n= log log n) arithmetic operations and O(n=(log n log log n)) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of (log n). In addition, we present the results of our imp...

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

Abstract We investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ degree 2, weight $k,$ level $N$. First, assuming that is a eigenform not Saito–Kurokawa type, we prove an improved bound in the $k$-aspect for smallest prime at which its eigenvalue negative. Secondly, show there are infinitely many sign changes amon...