Výsledky vyhledávání - "Mathematics::Number Theory"

Effective rational approximation on spheres

Autor: Zouhair Ouaggag

Publikováno v: Journal of Number Theory. 249:183-208

We prove an effective estimate for the counting function of Diophantine approximants on the sphere S$^n$. We use homogeneous dynamics on the space of orthogonal lattices, in particular effective equidistribution results and non-divergence estimates f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0a7b27d0d8216240b36d09dea74c70e
https://doi.org/10.1016/j.jnt.2023.02.015

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Overconvergent Hilbert modular forms via perfectoid modular varieties

Autor: Birkbeck, Christopher, Heuer, Ben, Williams, Chris

Publikováno v: Annales de l'Institut Fourier. :1-86

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex Hilbert modul

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38fa9b2ce39bab0c19446a1976f36d7d
https://doi.org/10.5802/aif.3560

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ZEROS OF DERIVATIVES OF L-FUNCTIONS IN THE SELBERG CLASS ON Re(s)< 1/2

Autor: Chaubey, Sneha, Khurana, Suraj Singh, Suriajaya, Ade Irma

Publikováno v: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 151(5):1855-1866

In this article, we show that the Riemann hypothesis for an $L$-function $F$ belonging to the Selberg class implies that all the derivatives of $F$ can have at most finitely many zeros on the left of the critical line with imaginary part greater than

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7be11b5c89713d2fb032d9d268bbb846
http://hdl.handle.net/2324/6790334

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The ℓ-adic hypergeometric function and associators

Autor: Furusho, Hidekazu

Publikováno v: Tunisian Journal of Mathematics. 5:1-29

We introduce an $\ell$-adic analogue of Gauss's hypergeometric function arising from the Galois action on the fundamental torsor of the projective line minus three points. Its definition is motivated by a relation between the KZ-equation and the hype

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::483dab49824e23901df2d8fba4398d26
https://doi.org/10.2140/tunis.2023.5.1

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Rank growth of elliptic curves over 𝑁-th root extensions

Autor: Shnidman, Ari, Weiss, Ariel

Publikováno v: Transactions of the American Mathematical Society, Series B. 10:482-506

Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$. We study the growth of the Mordell--Weil rank of $E$ after base change to the fields $K_d = F(\sqrt[2n]{d})$. If $E$ admits a $3$-isogeny, then we show that

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::15b9115ec536bd49e02fe860baf3bd01
https://doi.org/10.1090/btran/149

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Optimal lifting for the projective action of SL3(ℤ)

Autor: Kamber, Amitay, Lavner, Hagai

Publikováno v: Algebra & Number Theory. 17:749-774

Let $\epsilon>0$ and let $q$ be a prime going to infinity. We prove that with high probability given $x,y$ in the projective plane over the finite field $F_q$ there exists $\gamma$ in $SL_3(Z)$, with coordinates bounded by $q^{1/3+\epsilon}$, whose p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1790b91eb7cb95b1789b7c6b806ef369
https://doi.org/10.2140/ant.2023.17.749

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The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure

Autor: Daniel Gil Muñoz

Publikováno v: Daniel Gil Muñoz

For an odd prime number $p$, we consider degree $p$ extensions $L/K$ of $p$-adic fields with normal closure $\widetilde{L}$ such that the Galois group of $\widetilde{L}/K$ is the dihedral group of order $2p$. We shall prove a complete characterizatio

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa1b744083e9d4e28fb53763ba805bd5
https://doi.org/10.1016/j.jnt.2022.10.002

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On the connected components of Shimura varieties for CM unitary groups in odd variables

Autor: Yasuhiro Oki

Publikováno v: Journal of Number Theory. 245:1-64

We study the prime-to-$p$ Hecke action on the projective limit of the sets of connected components of Shimura varieties with fixed parahoric or Bruhat--Tits level at $p$. In particular, we construct infinitely many Shimura varieties for CM unitary gr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5506564eded5b770764912b760b736ee
https://doi.org/10.1016/j.jnt.2022.07.016

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Tame fundamental groups of pure pairs and Abhyankar’s lemma

Autor: Carvajal-Rojas, Javier, Stäbler, Axel

Publikováno v: Algebra & Number Theory. 17:309-358

Let $(R,\mathfrak{m}, k)$ be a strictly local normal $k$-domain of positive characteristic and $P$ be a prime divisor on $X=\text{Spec } R$. We study the Galois category of finite covers over $X$ that are at worst tamely ramified over $P$ in the sens

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2066fac2997122a94838f61183592865
https://doi.org/10.2140/ant.2023.17.309

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