Skip to main content

Kommende Vorträge

Posted in

Ausführliche Liste aller demnächst stattfindenden Vorträge und Seminare. Für eine Übersicht konsultieren Sie bitte auch den Kalender.

A proof of the prime number theorem IV

Posted in
Speaker: 
Efthymios Sofos
Zugehörigkeit: 
University of Leiden/MPIM
Datum: 
Don, 2018-09-20 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

A proof of the prime number theorem III

Posted in
Speaker: 
Efthymios Sofos
Zugehörigkeit: 
University of Leiden/MPIM
Datum: 
Mon, 2018-09-17 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

A proof of the prime number theorem II

Posted in
Speaker: 
Efthymios Sofos
Zugehörigkeit: 
University of Leiden/MPIM
Datum: 
Don, 2018-09-13 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

tba

Posted in
Speaker: 
Simon Myerson
Zugehörigkeit: 
University College London/MPIM
Datum: 
Mit, 2018-09-12 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A proof of the prime number theorem I

Posted in
Speaker: 
Efthymios Sofos
Zugehörigkeit: 
University of Leiden/MPIM
Datum: 
Mon, 2018-09-10 11:15 - 12:15
Location: 
MPIM Lecture Hall

 

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

tba

Posted in
Speaker: 
Maryna Viazovska
Zugehörigkeit: 
EPFL Lausanne
Datum: 
Fre, 2018-09-07 11:35 - 12:20
Location: 
MPIM Lecture Hall

Summing $\mu(n)$: a better elementary algorithm

Posted in
Speaker: 
Harald Helfgott
Zugehörigkeit: 
Universität Göttingen
Datum: 
Fre, 2018-09-07 10:15 - 11:00
Location: 
MPIM Lecture Hall

Joint with Lola Thompson.

Consider either of two related problems: determining the precise
number $\pi(x)$ of prime numbers $p\leq x$, and computing the Mertens
function $M(x) = \sum_{n\leq x} \mu(n)$, where $\mu$ is the Möbius function.

The two best algorithms known are the following:

Locally harmonic Maass forms and central $L$-values

Posted in
Speaker: 
Larry Rolen
Zugehörigkeit: 
Trinity College Dublin
Datum: 
Fre, 2018-09-07 09:25 - 10:10
Location: 
MPIM Lecture Hall

In this talk, we will discuss a relatively new modular-type object known as
a locally harmonic Maass form.
We will discuss recent joint work with Ehlen, Guerzhoy, and Kane with
applications to the theory of $L$-functions. In particular, we find
finite formulas for certain twisted central $L$-values of a family of
elliptic curves in terms of finite sums over canonical binary quadratic
forms. Applications to the congruent number problem will be given.

On smooth square-free numbers in arithmetic progressions

Posted in
Speaker: 
Igor E. Shparlinski
Zugehörigkeit: 
University of New South Wales
Datum: 
Don, 2018-09-06 16:30 - 17:00
Location: 
MPIM Lecture Hall

A.~Booker and C.~Pomerance (2017) have shown that any residue class modulo a prime $p\ge 11$ can be represented by a positive $p$-smooth square-free integer $s = p^{O(\log p)}$ with all prime factors up to $p$ and conjectured that in fact one can find such $s$ with $s = p^{O(1)}$. Using bounds on double Kloosterman sums due to M.~Z.~Garaev (2010) we prove this conjecture in a stronger form $s \le p^{3/2 + o(1)}$. Furthermore, using some additional arguments we show that for almost all primes $p$ one can replace $3/2$ with $4/3$.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A