For q ∈ C generic, we give an algorithmic construction of an ordered bijection between the set of H-primes of Oq (Mn(C)) and the sub-poset S of the (reverse) Bruhat order of the symmetric group S2n consisting of those permutations that move any integer by no more than n positions. Further, we describe the permutations that correspond via this bijection to rank t H-primes. More precisely, we est...

Let E be an elliptic curve defined over Q, of conductor N , and with complex multiplication. We prove unconditional and conditional asymptotic formulae for the number of ordinary primes p ! N , p ≤ x , for which the group of points of the reduction of E modulo p has square-free order. These results are related to the problem of finding an asymptotic formula for the number of primes p for which ...

Let K be a (commutative) field and consider a nonzero element q in K which is not a root of unity. In [5], Goodearl and Lenagan have shown that the number of H-primes in R = Oq (Mn(K)) which contain all (t+1)×(t+1) quantum minors but not all t× t quantum minors is a perfect square. The aim of this paper is to make precise their result: we prove that this number is equal to (t!)S(n+ 1, t+ 1), wh...

It is well-known that there are infinitely many irregular primes. We prove a quantitative version of this statement, namely the number of such primes p ≤ x is at least (1 + o(1)) log log x/ log log log x as x → ∞. We show that the same conclusion holds for the irregular primes corresponding to the Euler numbers. Under some conditional results from diophantine approximation, the above lower boun...

In the present paper, we derive some subordination and superordination results associated with a linear operator. Several sandwich-type results involving this operator are also proved. 2000 Mathematics Subject Classification: 30C45.

We prove sharp upper bounds for invariant measures of Markov processes in R associated with second-order elliptic differential operators with unbounded coefficients. Mathematics subject classification (2000): 35J70, 35B65, 47D07.

By using the method of differential subordinations, we derive certain sufficient conditions for strongly starlike functions associated with an integral operator. All these results presented here are sharp. 2000 Mathematics Subject Classification. Primary 30C45; Secondary 30A10.

In the present paper, we derive some subordination and superordination results associated with a linear operator. Several sandwich-type results involving this operator are also proved. 2000 Mathematics Subject Classification: 30C45.

We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place. 2000 Mathematics Subject Classification: 11F33.