Open AccessBook
A Course in Arithmetic
TLDR
In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.Abstract:
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.read more
Citations
More filters
Journal ArticleDOI
Complex dimensions of fractals and meromorphic extensions of fractal zeta functions
TL;DR: In this paper, the authors studied meromorphic extensions of distance and tube zeta functions, as well as of geometric zeta function of fractal strings, to arbitrary bounded subsets A of the N-dimensional Euclidean space.
Journal ArticleDOI
Even unimodular Euclidean lattices of dimension 32.II
TL;DR: In this paper, it was shown that even unimodular Euclidean lattices in dimension 32 with small root systems are generated by the vectors ν with (ν, ν) ⩽ 4.
Journal ArticleDOI
Generating and zeta functions, structure, spectral and analytic properties of the moments of Minkowski question mark function
TL;DR: In this paper, the moments of Minkowski question mark functions are investigated from the perspective of metric number theory, Hausdorff dimension, singularity and generalizations. And the results are analogous to the results obtained for objects associated with Maass wave forms: period functions, L-series, distributions, spectral properties.
Posted Content
On arithmetic Zariski pairs in degree 6
TL;DR: In this article, the authors define a topological invariant of complex projective plane curves, and present new examples of arithmetic Zariski pairs for algebraic arithmetic with projective planes.
Posted Content
Geometries in perturbative quantum field theory
TL;DR: In this article, a list of perturbative quantum geometries using the $c_2$-invariant in $\phi^4$ theory is presented, and the results from loop order 9 to 10 are extended to loop order 11 and partially orders 12 and 13.