Arcs with no more than two integer points on conics
Displaying 21 – 40 of 236
Arithmetical applications of an identity for the Vandermonde determinant
D. S. Ramana (2007)
Acta Arithmetica
Boundary conditions for expanding domains
Graeme Cohen (1975)
Acta Arithmetica
Changes of sign of error terms related to Euler's function and to divisor functions.
Y.-F. S. Pétermann (1986)
Commentarii mathematici Helvetici
Circles passing through five or more integer points
Shaunna M. Plunkett-Levin (2013)
Acta Arithmetica
We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let be the number of cyclic polygons...
Comment distribuer des points uniformément sur une sphère ? (D'après Lubotzky, Phillips et Sarnak)
Yves Colin de Verdière (1986/1987)
Séminaire de théorie spectrale et géométrie
Continuity Properties of Voronoi Domains.
H. Groemer (1971)
Monatshefte für Mathematik
Corrigendum to “On short sums of certain multiplicative functions”.
Bordellès, Olivier (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Counting problems and semisimple groups.
Eskin, Alex (1998)
Documenta Mathematica
Crible et 3-rang des corps quadratiques
Karim Belabas (1996)
Annales de l'institut Fourier
Considérons le cardinal de l’ensemble des racines cubiques de l’unité dans le groupe des classes de , où est un discriminant fondamental. Un résultat de Davenport et Heilbronn calcule la valeur moyenne de ces nombres quand varie. On obtient ici géométriquement une borne explicite pour le reste, avec la possibilité supplémentaire de restreindre les à des progressions arithmétiques. Des techniques de crible permettent alors d’évaluer la 3-partie des , où est pseudo-premier d’ordre . On...
Critical Dimensions for counting Lattice Points in Euclidean Annuli
L. Parnovski, N. Sidorova (2010)
Mathematical Modelling of Natural Phenomena
We study the number of lattice points in ℝd, d ≥ 2, lying inside an annulus as a function of the centre of the annulus. The average number of lattice points there equals the volume of the annulus, and we study the L1 and L2 norms of the remainder. We say that a dimension is critical, if these norms do not have upper and lower bounds of the same order as the radius goes to infinity. In [Duke Math. J., 107 (2001), No. 2, 209–238], it was proved that...
Croissance de certaines séries de Dirichlet et applications.
Patrick Sargos (1986)
Journal für die reine und angewandte Mathematik
Cyclic polygons of integer points
M. N. Huxley, S. V. Konyagin (2009)
Acta Arithmetica
Dedekind cotangent sums
Matthias Beck (2003)
Acta Arithmetica
Dedekind-Rademacher sums and lattice points in triangles and tetrahedra
Kenneth Rosen (1981)
Acta Arithmetica
Définition de paramètres d'équirépartition
André Gillet (1965/1966)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
Distribution of lattice points on hyperbolic surfaces
Vsevolod F. Lev (1996)
Acta Arithmetica
Let two lattices have the same number of points on each hyperbolic surface . We investigate the case when Λ’, Λ” are sublattices of of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.
Distribution of the linear flow length in a honeycomb in the small-scatterer limit.
Boca, Florin P. (2010)
The New York Journal of Mathematics [electronic only]
Divisors in a Dedekind domain
Javier Cilleruelo, Jorge Jiménez-Urroz (1998)
Acta Arithmetica
Ein Mittelwertsatz bei dreidimensionalen Gitterpunktproblemen
Peter Schmidt (1990)
Acta Arithmetica