Normal limiting distributions for systems of linear equations in random sets

Autor: Maximilian Wötzel, Juanjo Rué

Publikováno v: Gonzalez Herrera, A. (ed.), Discrete Mathematics Days 2022: Santander, Spain, July 4-6,2022, pp. 243-245
Linear Algebra and Its Applications, 649, 122-151
Linear Algebra and Its Applications, 649, pp. 122-151

We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a column vect

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9708a6efbab35f8adfbdbd6c810bcfc7
https://hdl.handle.net/2117/385698

p-adic L-functions and Euler systems

Autor: Velasco Falguera, Oriol

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

p-adic L-functions are variants of the classical L-functions, with a p-adic domain instead of the complex numbers. There are 2 ways to construct p-adic L-functions. The first one is purely analytic, by interpolation of the special values of the L-fun

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::b689b736457848cbfa5914548f5eebf8
https://hdl.handle.net/2117/372037

Extensions monògenes

Autor: Pedret Martínez, Francesc

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Aquest treball tracta de relacionar les extensions monògenes amb la teoria de corbes el·líptiques. Determinar si una extensió K/Q de grau n és monògena o no és equivalent a resoldre l'equació diofantina |I(X_1, \dots, X_{n - 1})| = 1, on I(X_

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::ab073a719247b7bbefb0b629ececd254
http://hdl.handle.net/2117/372002

An approximate structure theorem for small sumsets

Autor: Maximilian Wötzel, Matthew Coulson, Marcelo Campos, Oriol Serra

Publikováno v: Trends in Mathematics ISBN: 9783030838225
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Let A and B be randomly chosen s-subsets of the first n integers such that their sumset \(A+B\) has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions \(P_A\) and \(P_B\) with the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2859209604248709c2729e554835673b
https://hdl.handle.net/2117/369273

Finite slope triple product p-adic L-functions over totally real number fields

Autor: Santiago Molina

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

© 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ We construct p-adic L-functions associated with triples of finite slope p-adic families of quaternionic au

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d823131d54c3d66328e7920d9b33d23
https://arxiv.org/pdf/2003.08338.pdf