Subscribe: The Quarterly Journal of Mathematics - Advance Access
http://qjmath.oxfordjournals.org/rss/ahead.xml
Preview: The Quarterly Journal of Mathematics - Advance Access

The Quarterly Journal of Mathematics Advance Access





Published: Tue, 26 Sep 2017 00:00:00 GMT

Last Build Date: Tue, 26 Sep 2017 08:47:09 GMT

 



GEOMETRIC INTERPOLATION OF ENTROPY NUMBERS

2017-09-26

Abstract
We investigate whether the entropy numbers of an operator behave well under the complex interpolation between Hilbert spaces. We study geometric interpolation of entropy numbers of operators. We deliver a contribution to this problem by showing that an interpolation type inequality holds for these numbers. This is in contrast to the situation in Banach spaces, where by examples of Edmunds and Netrusov the entropy numbers do not interpolate well at least in the situation of the real method. As an application, we also present an interpolation estimate of single eigenvalues by single entropy numbers.



ON ABELIAN MULTIPLICATIVELY DEPENDENT POINTS ON A CURVE IN A TORUS

2017-09-26

Abstract
We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite set of primitive characters from Gmn to Gm restricted to the curve, and a finite set. We also introduce the notion of primitive multiplicative dependence and obtain a finiteness result for primitively multiplicatively dependent points defined over a so-called Bogomolov extension of a number field.



GAPS BETWEEN ZEROS OF THE RIEMANN ZETA-FUNCTION

2017-09-26

Abstract
We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).



A note on the geometry and topology of almost even-Clifford Hermitian manifolds

2017-09-21

Abstract
We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.