|
Date |
Speaker |
Title |
|
|
Sept 4 |
William D. Banks |
Do the zeros of one $L$-function know about the others? |
|
at 11:00am
in M1060
|
(University of Missouri)
|
In principle, the zeros of two distinct Dirichlet $L$-functions ought to be unrelated.
In fact, they turn out to be far more entangled than one expects, though not always.
My talk will survey some recent results in this circle of ideas, including
Linnik–Sprind\v{z}uk-type equivalences that reduce GRH to the vertical
distribution of the zeros of a single $L$-function. I will also describe in greater
depth some joint work with Kyle Loftus evaluating the twisted moment
$\sum_{\rho} x^{\rho} L(\rho,\chi_1)$ over the zeros $\rho$ of a second
$L$-function $L(s,\chi_2)$. Our results are unconditional and hold in short windows,
and they imply that no nontrivial linear combination of Dirichlet $L$-functions vanishes
on the entire zero set of another.
|
|
|
Sept 14 |
everyone |
Organizational meeting and problem session |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Please bring your favourite
(math) problems. Anyone with a problem to share will be given
about 5 minutes to present it. We will also choose most of the
speakers for the rest of the semester.
|
|
|
Sept 28 |
Andrew Fiori |
The Error Term in the Prime Number Theorem |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
In recent work with Mikko Jaskari we study the problem of finding tight explicit bounds on sums over zeros of $L$-functions near the $1$-line with a variety of zero-free regions and zero-density estimates.
As an application to demonstrate the techniques, we apply them to the case of the Riemann zeta function and the prime number theorem to obtain new best estimates on the error terms in the prime number theorem for large $x.$
We show that for $\log(x)\geq 3$ we have
\[|\psi(x)-x| < 0.239 \, x \exp\left(-0.1982767\left(1+\frac{\log\log\log(x)}{15\log\log(x)}\right) \frac{\log(x)^{3/5}}{\log\log(x)^{1/5}}\right)\] and
for $\log(x)>10^{15}$ we have
\[|\psi(x)-x| < (1.1485 {\times} 10^{-1154556} ) \, x \exp\left(\! -0.1982767\left(\! 1+\frac{\log\log\log(x)}{15\log\log(x)} \!\right)
\! \frac{\log(x)^{3/5}}{\log\log(x)^{1/5}} \!\right) . \]
In this talk I will explain how we obtain this result.
|
|
|
Oct 19 |
Sarobidy Razafimahatratra |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
|
Oct 26 |
Paul Péringuey |
Title TBA |
|
at 12:00pm
in M1060
|
(UNBC)
|
Abstract TBA
|
|
|
Nov 2 |
Melissa Huggan |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
|
Nov 16 |
Speaker TBA |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
|
Nov 23 |
Speaker TBA |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
|
Nov 30 |
Speaker TBA |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
|
Dec 7 |
Speaker TBA |
Title TBA |
|
at 12:00pm
in M1060
|
(University of Lethbridge)
|
Abstract TBA
|
|
