A cardinal λ is called ω-inaccessible if for all μ < λ we have μ < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forcing...

The Noetherian type of a space is the least κ for which the space has a κop-like base, i.e., a base in which no element has κ-many supersets. We prove some results about Noetherian types of (generalized) ordered spaces and products thereof. For example: the density of a product of not-too-many compact linear orders never exceeds its Noetherian type, with equality possible only for singular Noet...

Let P be a property (or, equivalently, a class) of topological spaces. A space X is called P-bounded if every subspace of X with (or in) P has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω-bounded. In this paper we present a systematic study of the interrelations of these two known “boundedness” concepts with P-boundedness where P is ...

UDC 511.3+517.43+519.45 For the Riemann zeta-function on the critical line the terminal estimate have been proved, which had been conjectured by Lindelöf at the beginning of this Centure. The proof is based on the authors relations which connect the bilinear forms of the eigenvalues of the Hecke operators with sums of the Kloosterman sums. By the way, it is proved that for the Hecke series (whi...

In this paper we use a natural forcing to construct a left-separated topology on an arbitrary cardinal κ. The resulting left-separated space Xκ is also 0-dimensional T2, hereditarily Lindelöf, and countably tight. Moreover if κ is regular then d(Xκ) = κ, hence κ is not a caliber of Xκ, while all other uncountable regular cardinals are. This implies that some results of [A] and [JSz] are, consis...

The Phragmén-Lindelöf theorem for Lp-viscosity solutions of fully nonlinear second order elliptic partial differential equations with unbounded coefficients and inhomogeneous terms is established.

For a fixed SL(3,Z) Maass form φ, we consider the family of L-functions L(φ× uj, s) where uj runs over the family of Hecke-Maass cusp forms on SL(2,Z). We obtain an estimate for the second moment of this family of L-functions at the special points 1 2 + itj consistent with the Lindelöf Hypothesis. We also obtain a similar upper bound on the sixth moment of the family of Hecke-Maass cusp forms a...