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Creators/Authors contains: "Harcos, Gergely"

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  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). 
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    Free, publicly-accessible full text available March 22, 2026
  2. ; (, 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). 
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  3. ; ; ; (, 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. 
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  4. ; ; ; (, Journal de Mathématiques Pures et Appliquées)
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  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. 
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