Hyperbolic Angles from Heegner Points

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10508553" target="_blank" >RIV/00216208:11320/25:10508553 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Bsq3TQNcoo" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Bsq3TQNcoo</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1307/mmj/20226321" target="_blank" >10.1307/mmj/20226321</a>

Result language
angličtina
Original language name
Hyperbolic Angles from Heegner Points
Original language description
We study lattice points on hyperbolic circles centered at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angles of such points equidistribute on the unit circle. To prove this, we establish a connection between lattice points and algebraic integers in the associated field having norm of a special form and satisfying a congruence condition. As a by-product of this, we obtain an explicit formulation of the classical hyperbolic circle problem as a shifted convolution sum for the function that counts the number of algebraic integers with given norm. Along the way, we also prove a lower bound for shifted Bnumbers, which is done by sieve methods.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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