skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Harcos, Gergely"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Let 𝜋 and π ′ \pi^{\prime}be cuspidal automorphic representations of GL ⁢ ( n ) \mathrm{GL}(n)and GL ⁢ ( n ′ ) \mathrm{GL}(n^{\prime})with unitary central characters.We establish a new zero-free region for all GL ⁢ ( 1 ) \mathrm{GL}(1)-twists of the Rankin–Selberg 𝐿-function L ⁢ ( s , π × π ′ ) L(s,\pi\times\pi^{\prime}), generalizing Siegel’s celebrated work on Dirichlet 𝐿-functions.As an application, we prove the first unconditional Siegel–Walfisz theorem for the Dirichlet coefficients of − L ′ ⁢ ( s , π × π ′ ) / L ⁢ ( s , π × π ′ ) -L^{\prime}(s,\pi\times\pi^{\prime})/L(s,\pi\times\pi^{\prime}).Also, for n ≤ 8 n\leq 8, we extend the region of holomorphy and nonvanishing for the twisted symmetric power 𝐿-functions L ⁢ ( s , π , Sym n ⊗ χ ) L(s,\pi,\mathrm{Sym}^{n}\otimes\chi)of any cuspidal automorphic representation of GL ⁢ ( 2 ) \mathrm{GL}(2). 
    more » « less
    Free, publicly-accessible full text available March 22, 2026
  2. ; ; ; (, American Journal of Mathematics)
    We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations are uniform in the volume and spectral aspects. 
    more » « less
    Full Text Available 
  3. ; (, Science China Mathematics)
    Abstract LetL/Kbe a Galois extension of number fields with Galois groupG. We show that if the density of prime ideals inKthat split totally inLtends to 1/∣G∣ with a power saving error term, then the density of prime ideals inKwhose Frobenius is a given conjugacy classC⊂Gtends to ∣C∣/∣G∣ with the same power saving error term. We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζL(s)/ζK(s). 
    more » « less
    Full Text Available 
  4. ; ; ; (, Journal de Mathématiques Pures et Appliquées)
    Full Text Available 
  5. ; ; (, International Mathematics Research Notices)
    Abstract We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers. 
    more » « less
    Full Text Available