Non-commutative Markov processes in free groups factors, related to Berezin's quantization and automorphic forms.
Noncongruence subgroups of the Hecke groups G (...).
Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
Noncontinuable power series
Non-converging continued fractions related to the Stern diatomic sequence
Noncyclotomic -extensions of imaginary quadratic fields.
Non-degenerate Hilbert cubes in random sets
A slight modification of the proof of Szemerédi’s cube lemma gives that if a set satisfies , then must contain a non-degenerate Hilbert cube of dimension . In this paper we prove that in a random set determined by for , the maximal dimension of non-degenerate Hilbert cubes is a.e. nearly and determine the threshold function for a non-degenerate -cube.
Non-divisibility of some multiplicative functions
Non-existence and splitting theorems for normal integral bases
We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower forces the tower to be split in a very strong sense.
Nonexistence of a geometric progression that contains four triangular numbers.
Nonexistence of almost Moore digraphs of diameter three.
Nonexistence of permutation binomials of certain shapes.
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Non-existence of singular cusp forms
Nonexistence of twentieth power residue difference sets
Nonextendibility of -triples of the form .
Non-free Projective Modules Over IH[X, Y] and Stable Bundles Over IP2(...).
Non-integer lattice tilings by (k, n) truncated crosses.
Noninvariant base change identities
Non-Kähler compact complex manifolds associated to number fields
For algebraic number fields with real and complex embeddings and “admissible” subgroups of the multiplicative group of integer units of we construct and investigate certain -dimensional compact complex manifolds . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when . In particular we disprove a conjecture of I. Vaisman.