Estimates on the decay of the Laplace–Pólya integral
The Laplace–Pólya integral, defined by , appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer . Our main result establishes a lower bound for the ratio which extends and generalises the previous esti...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2025
|
| Sorozat: | BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
|
| Tárgyszavak: | |
| doi: | 10.1112/blms.70157 |
| mtmt: | 36281398 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37409 |
| Tartalmi kivonat: | The Laplace–Pólya integral, defined by , appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer . Our main result establishes a lower bound for the ratio which extends and generalises the previous estimates of Lesieur and Nicolas [23], and provides a natural counterpart to the upper estimate established in our previous work [2]. We derive the statement by purely combinatorial, elementary arguments. As a corollary, we deduce that no subdiagonal central sections of the unit cube are extremal, apart from the minimal, maximal, and the main diagonal sections. We also prove several consequences for Eulerian numbers. |
|---|---|
| ISSN: | 0024-6093 |