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# Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 200

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## Multi angle  Prime numbers with preassigned digits Swaenepoel, Cathy (Auteur de la Conférence) | CIRM (Editeur )

Bourgain (2015) estimated the number of prime numbers with a proportion $c$ > 0 of preassigned digits in base 2 ($c$ is an absolute constant not specified). We present a generalization of this result in any base $g$ ≥ 2 and we provide explicit admissible values for the proportion $c$ depending on $g$. Our proof, which adapts, develops and refines Bourgain’s strategy, is based on the circle method and combines techniques from harmonic analysis together with results on zeros of Dirichlet $L$-functions, notably a very sharp zero-free region due to Iwaniec.
Bourgain (2015) estimated the number of prime numbers with a proportion $c$ > 0 of preassigned digits in base 2 ($c$ is an absolute constant not specified). We present a generalization of this result in any base $g$ ≥ 2 and we provide explicit admissible values for the proportion $c$ depending on $g$. Our proof, which adapts, develops and refines Bourgain’s strategy, is based on the circle method and combines techniques from harmonic analysis ...

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## Multi angle  Monogenic cubic fields and local obstructions Shnidman, Ari (Auteur de la Conférence) | CIRM (Editeur )

A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic. This uses new results on ranks of Selmer groups of elliptic curves in twist families.
A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are ...

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## Multi angle  On Epstein's zeta function and related random functions Södergren, Anders (Auteur de la Conférence) | CIRM (Editeur )

In this talk I will discuss questions concerning the asymptotic behavior of the Epstein zeta function $E_{n}\left ( L, s \right )$ in the limit of large dimension $n$. In particular I will be interested in the behavior of $E_{n}\left ( L, s \right )$ for a random lattice $L$ of large dimension $n$ and $s$ a complex number in the critical strip. Along the way we will encounter certain random functions that are closely related to $E_{n}\left ( L, s \right )$ and interesting in their own right.

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