Výsledky vyhledávání - "Leo Goldmakher"

Akademický článek

Khovanskii's theorem and effective results on sumset structure

Autor: Michael J. Curran, Leo Goldmakher

Publikováno v: Discrete Analysis (2021)

Khovanskii's theorem and effective results on sumset structure, Discrete Analysis 2021:27, 25 pp. Let $A$ be a subset of an Abelian group. The $n$-_fold sumset_ $nA$ of $A$ is the set $\{a_1+\dots+a_n:a_1,\dots,a_n\in A\}$. Much of additive combinat

Externí odkaz: https://doaj.org/article/0bbdecbe640a4249b093c6cc71cbee5b

Zobrazit plný text záznamu

The frequency and the structure of large character sums

Autor: Andrew Granville, Dimitris Koukoulopoulos, Jonathan Bober, Leo Goldmakher

Publikováno v: Bober, J, Goldmakher, L, Granville, A & Koukoulopoulos, D 2018, ' The frequency and the structure of large character sums ', Journal of the European Mathematical Society, vol. 20, no. 7, pp. 1759-1818 . https://doi.org/10.4171/JEMS/799

Let $M(\chi)$ denote the maximum of $|\sum_{n\le N}\chi(n)|$ for a given non-principal Dirichlet character $\chi \pmod q$, and let $N_\chi$ denote a point at which the maximum is attained. In this article we study the distribution of $M(\chi)/\sqrt{q

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5340371e3028b01dcf05fee57de9b5ce
https://doi.org/10.4171/jems/799

Zobrazit plný text záznamu

Pólya–Vinogradov and the least quadratic nonresidue

Autor: Leo Goldmakher, Jonathan Bober

Publikováno v: Bober, J & Goldmakher, L 2016, ' Pólya–Vinogradov and the least quadratic nonresidue ', Mathematische Annalen, vol. 366, no. 1, pp. 853-863 . https://doi.org/10.1007/s00208-015-1353-2

It is well-known that cancellation in short character sums (e.g. Burgess’ estimates) yields bounds on the least quadratic nonresidue. Scant progress has been made on short character sums since Burgess’ work, so it is desirable to find another app

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da179b93e3b9674963d44d393834f839
https://doi.org/10.1007/s00208-015-1353-2

Zobrazit plný text záznamu

Large even order character sums

Autor: Leo Goldmakher, Youness Lamzouri

Publikováno v: Proceedings of the American Mathematical Society. 142:2609-2614

A classical theorem of Paley asserts the existence of an infinite family of quadratic characters whose character sums become exceptionally large. In this paper, we establish an analogous result for characters of any fixed even order. Previously our b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00569c697ba7aa79ed6434a08f3ba6e4
https://doi.org/10.1090/s0002-9939-2014-11990-3

Zobrazit plný text záznamu

Improving the Burgess bound via Polya-Vinogradov

Autor: Leo Goldmakher, Elijah Fromm

We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the secon

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::004a0839d5b2c935757aa30ce08a0708

Zobrazit plný text záznamu

Mock characters and the Kronecker symbol

Autor: Leo Goldmakher, Jean-Paul Allouche

We introduce and study a family of functions we call the "mock characters". These functions satisfy a number of interesting properties, and of all completely multiplicative arithmetic functions seem to come as close as possible to being Dirichlet cha

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc09878f3f8c62e916699feea6c30f03
http://arxiv.org/abs/1608.03957

Zobrazit plný text záznamu

L-Functions with n-th-Order Twists

Autor: Valentin Blomer, Benoit Louvel, Leo Goldmakher

Publikováno v: International Mathematics Research Notices. 2014:1925-1955

Let K be a number field containing the n-th roots of unity for some n > 2. We prove a uniform subconvexity result for a family of double Dirichlet series built out of central values of Hecke L-functions of n-th order characters of K. The main new ing

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f15c561e4c5ab9fb4d14f7750c3e19b1
https://doi.org/10.1093/imrn/rns257

Zobrazit plný text záznamu

Character Sums to Smooth Moduli are Small

Autor: Leo Goldmakher

Publikováno v: Canadian Journal of Mathematics. 62:1099-1115

Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham-Ringrose and Iwaniec, we improve the Polya-Vinogradov ine

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6b90e05b4de243bdff7603dd27087fa
https://doi.org/10.4153/cjm-2010-047-9

Zobrazit plný text záznamu

On the spectral distribution of large weighted random regular graphs

Autor: Kesinee Ninsuwan, Leo Goldmakher, Steven J. Miller, Cap Khoury

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large $d$-regular gr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ab91f575939ac15899063266f982e37
http://arxiv.org/abs/1306.6714

Zobrazit plný text záznamu

A quadratic large sieve inequality over number fields

Autor: Leo Goldmakher, Benoit Louvel

We formulate and prove a large sieve inequality for quadratic characters over a number field. To do this, we introduce the notion of an n-th order Hecke family. We develop the basic theory of these Hecke families, including versions of the Poisson su

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cfb3d40093c036a48a8645175575801c
http://resolver.sub.uni-goettingen.de/purl?gs-1/11577

Zobrazit plný text záznamu

Vyhledávací nástroje:

Upřesnit hledání