# Upcoming Talks

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Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## A proof of the prime number theorem IV

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Speaker:
Efthymios Sofos
Affiliation:
University of Leiden/MPIM
Date:
Thu, 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

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Speaker:
Efthymios Sofos
Affiliation:
University of Leiden/MPIM
Date:
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

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Speaker:
Efthymios Sofos
Affiliation:
University of Leiden/MPIM
Date:
Thu, 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

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Speaker:
Simon Myerson
Affiliation:
University College London/MPIM
Date:
Wed, 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

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Speaker:
Efthymios Sofos
Affiliation:
University of Leiden/MPIM
Date:
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

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Speaker:
Maryna Viazovska
Affiliation:
EPFL Lausanne
Date:
Fri, 2018-09-07 11:35 - 12:20
Location:
MPIM Lecture Hall

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

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Speaker:
Harald Helfgott
Affiliation:
Universität Göttingen
Date:
Fri, 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

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Speaker:
Larry Rolen
Affiliation:
Trinity College Dublin
Date:
Fri, 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

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Speaker:
Igor E. Shparlinski
Affiliation:
University of New South Wales
Date:
Thu, 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 $4/3$.

## Speed Talks

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Date:
Thu, 2018-09-06 15:05 - 15:50
Location:
MPIM Lecture Hall
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