Analytic number theory seminar at GTIIT
Analytic number theory seminar at Guangdong Technion – Israel Institute of Technology (GTIIT),
Shantou, China.
Dates: 13–15 March 2026
Venue: Guangdong Technion – Israel Institute of Technology (GTIIT)
Format: Research talks in analytic number theory.
Preliminary schedule
| Date | Time | Speaker | Title |
|---|---|---|---|
| Friday, 13 March | 18.30 | Dinner | |
| Saturday, 14 March | 10.00 | Chan leong Kuan (Sun Yat-sen University) | Subconvexity for twisted GL(3) L-functions |
| 11.00 | Yingnan Wang (Shenzhen University) | Sign changes of Fourier coefficients on GL(m). | |
| 12.00-14.00 | Lunch | ||
| 14.00 | Yuk-Kam Lau (The University of Hong Kong) | Distribution of the error term in the Dirichlet divisor problem | |
| 15.00 | Shaoyun Yi (Xiamen University) | Some results on classical and adelic Eisenstein series | |
| 16.00 | Nikita Kalinin (Guangdong Technion) | Zeta-series for convex domains and its pole at s=2/3 | |
| Sunday, 15 March | 10.00 | Ezra Waxman (Afeka) | Lattice Points in Thin Sectors |
| 11.00 | Discussions |
Place: SC-E2-103 (South campus, educational building)
Talks
Subconvexity for twisted GL(3) L-functions
Speaker: Chan leong Kuan (Sun Yat-sen University)
Abstract:
Using a variant of circle method and conductor lowering trick
originally devised by Munshi, we obtain subconvex bounds for twisted
GL(3) L-functions, in the character and (t)-aspects simultaneously.
This is joint work with E.M. Kıral and D. Lesesvre.
Sign changes of Fourier coefficients on GL(m).
Speaker: Yingnan Wang
Abstract:
In this talk, we will survey some results on sign changes of Fourier coefficients
(Hecke eigenvalues) of holomorphic Hecke eigenforms on GL_2 and Hecke-Maass forms on GL_m (m>=2).
Then we will introduce some statistical results on sign changes of Fourier
coefficients of Hecke-Maass forms on GL_m (m>=3). For most Hecke-Maass cusp forms,
we give the asymptotic number of nonvanishing coefficients, show that there is a
positive proportion of sign changes among them, when these are real, and describe
the asymptotic density of these signs. This talk is based on a joint work with
Didier Lesesvre and Ming Ho Ng
Distribution of the error term in the Dirichlet divisor problem
Speaker: Yuk-Kam Lau
Abstract:
Three decades ago, Heath-Brown resolved the question of whether a limiting
distribution function exists for the normalized error term in the Dirichlet divisor problem.
In this talk, we will review his groundbreaking work and the subsequent developments.
In particular, we will discuss recent advances by Lamzouri.
Some results on classical and adelic Eisenstein series
Speaker: Shaoyun Yi (Xiamen University)
Abstract:
In this talk, we will discuss the classical Siegel Eisenstein series
of weight (k) and degree (2) within an adelic framework, mainly applying the
method known as “Hecke summation”. In the process, we recover the classical
Fourier expansion of the Siegel Eisenstein series from an adelic point
of view. One of our goals is to determine the automorphic representations
associated to these Siegel Eisenstein series, particularly for the case of weight
(k = 2), where the underlying global representation is highly reducible.
First, we will give a quick introduction to the necessary background and motivation for this work. Next, we will briefly review recent results in the study of classical and adelic Eisenstein series for GL(2) (the degree (1) case), which may be viewed as a toy example. Finally, we will present an overview of our ongoing work on the Siegel Eisenstein series of degree (2). These are joint works with Manami Roy and Ralf Schmidt.
Zeta-series for convex domains and its pole at s=2/3
Speaker: Nikita Kalinin (Guangdong Technion-Israel Institute of Technology)
Abstract:
Let $\Omega\subset\mathbb R^2$ be a bounded convex domain. To $\Omega$ we associate a Dirichlet-type series
$
F_\Omega(s)=\sum_{v\in\mathbb Z^2} f_\Omega(v)^s,$
where the sum ranges over primitive lattice vectors and $f_\Omega(v)$
is a natural weight determined by the support function of $\Omega$ in directions of $v$ and $x_v, y_v$ where $x_v+y_v=v$ and $det(u,v)=1$.
Beyond its lattice-geometric origin, $F_\Omega(s)$ exhibits a modular symmetry:
it is $SL(2,\mathbb Z)$-invariant up to explicitly controlled holomorphic correction terms.
We prove that $F_\Omega(s)$ admits a meromorphic continuation to the half-plane $\Re(s)> \tfrac12$, and that it has a \emph{simple pole} at $s=\tfrac23$. The leading term is geometric: the residue at $s=\tfrac23$ is proportional to the \emph{affine length} of $\partial\Omega$ (the equi-affine perimeter), revealing a new bridge between analytic continuation of lattice sums and affine differential geometry of convex curves. Joint work with M.~Shkolnikov and E.~Lupercio.
Lattice Points in Thin Sectors
Speaker: Ezra Waxman
Abstract:
On the circle of radius R centred at the origin, consider a thin
sector about the fixed line y = \alpha x with edges given by the lines
$y = (\alpha \pm \epsilon) x$, where $\epsilon = \epsilon_R \rightarrow 0$ as $R \to \infty$.
We discuss an asymptotic count for $S_{\alpha}(\epsilon,R)$, the number of integer
lattice points lying in such a sector, and moreover present results concerning the variance of such lattice points across sectors
More details will be circulated by email.
Organiser: Nikita Kalinin (GTIIT), Ezra Waxman (Afeka)