Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Sandro Bettin"'
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case $m,n\leq2$.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e72d9fee5bed7952e4fd605f4aabc0d1
http://arxiv.org/abs/2109.00745
http://arxiv.org/abs/2109.00745
Autor:
Kevin Destagnol, Sandro Bettin
Publikováno v:
Mathematika
Using recent work of the first author~\cite{Bet}, we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in $\mathbb{P}^2 \times \mathbb{P}^2$ with bihomogene
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::186fc2f16629dc2344a9095c782fa79d
https://doi.org/10.1112/s0025579319000159
https://doi.org/10.1112/s0025579319000159
Publikováno v:
Bettin, S, Bui, H, Li, X & Radziwill, M 2020, ' A quadratic divisor problem and moments of the Riemann zeta-function ', Journal of the European Mathematical Society, vol. 22, pp. 3953–3980 . https://doi.org/10.4171/JEMS/999
We estimate asymptotically the fourth moment of the Riemann zeta-function twisted by a Dirichlet polynomial of length $T^{\frac14 - \varepsilon}$. Our work relies crucially on Watt's theorem on averages of Kloosterman fractions. In the context of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b88ed8cdccb2e11fb61b9551c8190b14
https://pure.manchester.ac.uk/ws/files/173978895/BettinBuiLiRadziwill_twisted_fourth_moment.pdf
https://pure.manchester.ac.uk/ws/files/173978895/BettinBuiLiRadziwill_twisted_fourth_moment.pdf
Autor:
Sandro Bettin, Sary Drappeau
Publikováno v:
Mathematische Annalen
Mathematische Annalen, 2022, 382 (3-4), pp.1631-1679. ⟨10.1007/s00208-021-02288-2⟩
Mathematische Annalen, Springer Verlag, In press
Mathematische Annalen, 2022, 382 (3-4), pp.1631-1679. ⟨10.1007/s00208-021-02288-2⟩
Mathematische Annalen, Springer Verlag, In press
We obtain an exact modularity relation for the $q$-Pochhammer symbol. Using this formula, we show that Zagier's modularity conjecture for a knot $K$ essentially reduces to the arithmeticity conjecture for $K$. In particular, we show that Zagier's con
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::475606caecb97af692a4cbe2c94f00d9
https://hal.archives-ouvertes.fr/hal-02998581/document
https://hal.archives-ouvertes.fr/hal-02998581/document
Autor:
Sandro Bettin, Sary Drappeau
Publikováno v:
Ramanujan Journal
Ramanujan Journal, 2022, 57 (2), pp.849-861. ⟨10.1007/s11139-020-00362-y⟩
Ramanujan Journal, 2022, 57 (2), pp.849-861. ⟨10.1007/s11139-020-00362-y⟩
We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals $$ {\mathcal I}(t) = \int_{\mathbb R}({\rm e}^{it\phi(x)}-1) {\rm d} \mu(x) $$ where $\mu$ is a probability measure on $\mathbb{R}$ and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a535b5208c8adbc8b44fe02c7272ac23
https://hal.archives-ouvertes.fr/hal-02998544/document
https://hal.archives-ouvertes.fr/hal-02998544/document
Given two sets of natural numbers $\mathcal{A}$ and $\mathcal{B}$ of natural density $1$ we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\mathcal{B}\}$ also has natural density $1$. On the other hand, for any
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d8783314b1b585f5965bf11e21dccf2
Given a real number τ, we study the approximation of τ by signed harmonic sums σ N ( τ ) : = ∑ n ≤ N s n ( τ ) / n , where the sequence of signs ( s N ( τ ) ) N ∈ N is defined “greedily” by setting s N + 1 ( τ ) : = + 1 if σ N ( τ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f18c827d15d1d2a463a48b5bad4c53d8
http://hdl.handle.net/11567/1011900
http://hdl.handle.net/11567/1011900
Autor:
Sandro Bettin, Sary Drappeau
Publikováno v:
Journal de Théorie des Nombres de Bordeaux
Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2020, 32 (1), pp.217-230. ⟨10.5802/jtnb.1119⟩
Journal de Théorie des Nombres de Bordeaux, 2020, 32 (1), pp.217-230. ⟨10.5802/jtnb.1119⟩
Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2020, 32 (1), pp.217-230. ⟨10.5802/jtnb.1119⟩
Journal de Théorie des Nombres de Bordeaux, 2020, 32 (1), pp.217-230. ⟨10.5802/jtnb.1119⟩
International audience; We prove the existence of reciprocity formulae for sums of the form $\sum_{m=1}^{k-1}f\pr{\frac{m}{k}}\cot\pr{\pi \frac{m h}k}$ where $f$ is a piecewise~$C^1$ function, featuring an alternating phenomenon not visible in the cl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f4097171bec8014bc61a8371b2eb73ba
http://hdl.handle.net/11567/1062898
http://hdl.handle.net/11567/1062898
Publikováno v:
Comptes Rendus Mathematique. 356:1062-1074
For every $\tau\in\mathbb{R}$ and every integer $N$, let $\mathfrak{m}_N(\tau)$ be the minimum of the distance of $\tau$ from the sums $\sum_{n=1}^N s_n/n$, where $s_1, \ldots, s_n \in \{-1, +1\}$. We prove that $\mathfrak{m}_N(\tau) < \exp\!\big(-C(
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad59e4c9825ea436cc5665a1f765f12b
https://doi.org/10.1016/j.crma.2018.11.007
https://doi.org/10.1016/j.crma.2018.11.007
Autor:
Sandro Bettin
Publikováno v:
Algebra Number Theory 13, no. 2 (2019), 251-300
For $a/q\in\mathbb{Q}$ the Estermann function is defined as $D(s,a/q):=\sum_{n\geq1}d(n)n^{-s}\operatorname{e}(n\frac aq)$ if $\Re(s)>1$ and by meromorphic continuation otherwise. For $q$ prime, we compute the moments of $D(s,a/q)$ at the central poi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92c3ac267a4b439c8508d29babe44470
https://projecteuclid.org/euclid.ant/1553565643
https://projecteuclid.org/euclid.ant/1553565643