[Turkmath:6630] Seminer-Igor Shparlinski (University of New South Wales, Australia)-Bilecik-15 Ekim

[Ilker Inam]

Değerli Liste Üyeleri,



Bilecik Şeyh Edebali Üniversitesi Fen Fakültesi Matematik Bölümü Cebir ve
Sayılar Teorisi Anabilim dalı öğretim üyeleri tarafından kurulan “Bilecik
Algebra & Number Theory (BANT)” grubu tarafından organize edilen seminer
serilerinin yeni dönemi başlıyor. Bu dönemin ilk konuşması *15 Ekim** 2024
Salı günü* online olarak zoom üzerinden düzenlenecektir.


Etkinliğin web sitesi: https://bilecikalgebranumbertheory.github.io/ dir.



İlk konuşmacı University of New South Wales'in (Avustralya) değerli öğretim
üyesi *Igor Shparlinski* olacaktır ve konuşma bilgileri aşağıda yer
almaktadır.



*Konuşma Adı:* Moments and non-vanishing of $L$-functions over thin
subgroups
*Özet:* Moments and non-vanishing of $L$-functions over thin subgroups. We
obtain an asymptotic formula for all moments of Dirichlet $L$-functions
$L(1,\chi)$ modulo $p$ when averaged over a subgroup of characters $\chi$
of size $(p-1)/d$ with $\varphi(d)=o(\log p)$. Assuming the infinitude of
Mersenne primes, the range of our result is optimal and improves and
generalises the previous result of S.~Louboutin and M.~Munsch (2022) for
second moments. We also give an asymptotic formula for the second moment of
$L(1/2,\chi)$ over subgroups of characters of similar size. This leads to
non-vanishing results which in some cases improve those of E. Fouvry, E.
Kowalski and P. Michel (2023). Additionally, we prove that, in both cases,
we can take much smaller subgroups for almost all primes $p$. Our method
relies on pointwise and average estimates on small solutions of linear
congruences which in turn leads us to use and modify some results of
J.~Bourgain, S.~V.~Konyagin and I.~E.~Shparlinski (2008) on product sets of
Farey fractions. Joint work with Marc Munsch.

*Tarih: 15/10/2024 *

*Saat: 10:00 İstanbul / 09:00 Berlin / 08:00 Londra *



Katılım için linkte yer alan form doldurulması yeterlidir,

Form linki: https://forms.gle/Ds3XNZXn1YNxapJU9



Zoom linki formu doldurduktan sonra email ile paylaşılacaktır. Etkinlik
posteri ekte yer almaktadır.



Saygılarımla,

Prof.Dr. İlker İnam

Düzenleme komitesi adına.





—————————————————————



Dear list members,



The "Bilecik Algebra & Number Theory (BANT)" group, founded by the faculty
members of the Department of Algebra and Number Theory at Bilecik Seyh
Edebali University's Faculty of Science, will host its first seminar of the
semester on *Tue, October 15, 2024*. The event will be conducted online via
Zoom.

The website for the event is:  https://bilecikalgebranumbertheory.github.io/
.



The inaugural speaker will be Igor Shparlinski, a faculty member at
University of New South Wales, Australia. Details of the presentation are
provided below.



*Title: *Moments and non-vanishing of $L$-functions over thin subgroups

*Abstract: *Moments and non-vanishing of $L$-functions over thin subgroups.
We obtain an asymptotic formula for all moments of Dirichlet $L$-functions
$L(1,\chi)$ modulo $p$ when averaged over a subgroup of characters $\chi$
of size $(p-1)/d$ with $\varphi(d)=o(\log p)$. Assuming the infinitude of
Mersenne primes, the range of our result is optimal and improves and
generalises the previous result of S.~Louboutin and M.~Munsch (2022) for
second moments. We also give an asymptotic formula for the second moment of
$L(1/2,\chi)$ over subgroups of characters of similar size. This leads to
non-vanishing results which in some cases improve those of E. Fouvry, E.
Kowalski and P. Michel (2023). Additionally, we prove that, in both cases,
we can take much smaller subgroups for almost all primes $p$. Our method
relies on pointwise and average estimates on small solutions of linear
congruences which in turn leads us to use and modify some results of
J.~Bourgain, S.~V.~Konyagin and I.~E.~Shparlinski (2008) on product sets of
Farey fractions. Joint work with Marc Munsch.

*Date: October 15, 2024, Tuesday*

*Time: 10:00 Istanbul / 09:00 Berlin / 08:00 London *



To participate, simply fill out the form at the following link:

Form Link: https://forms.gle/Ds3XNZXn1YNxapJU9



The Zoom link will be shared via email after filling out the form. The
event poster is attached.



Best regards,

Prof.Dr. Ilker Inam

On behalf of the organizing committee
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