<div dir="ltr"><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Değerli Liste Üyeleri, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">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</font><span style="font-family:arial,sans-serif"> <b>15 Ekim</b></span><b style="font-family:arial,sans-serif"> 2024 Salı günü</b><span style="font-family:arial,sans-serif"> online olarak zoom üzerinden düzenlenecektir. </span></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><br></font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Etkinliğin web sitesi: <a href="https://bilecikalgebranumbertheory.github.io/" target="_blank">https://bilecikalgebranumbertheory.github.io/</a> dir. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">İlk konuşmacı University of New South Wales'in (Avustralya) değerli öğretim üyesi<span> </span><b><span>Igor Shparlinski</span></b><span> </span>olacaktır ve konuşma bilgileri aşağıda yer almaktadır. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="monospace"><b>Konuşma Adı:</b> <span style="color:rgb(36,41,46)">Moments and non-vanishing of $L$-functions over thin subgroups<br></span><b>Özet:</b> <span style="color:rgb(36,41,46)">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.</span></font></p><div><font face="arial, sans-serif"><b><br></b></font><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Tarih: 15/10/2024 </font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Saat: 10:00 İstanbul / 09:00 Berlin / 08:00 Londra </font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Katılım için linkte yer alan form doldurulması yeterlidir, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Form linki: </font><a href="https://forms.gle/Ds3XNZXn1YNxapJU9" target="_blank">https://forms.gle/Ds3XNZXn1YNxapJU9</a> </p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Zoom linki formu doldurduktan sonra email ile paylaşılacaktır. Etkinlik posteri ekte yer almaktadır. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Saygılarımla, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Prof.Dr. İlker İnam</font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Düzenleme komitesi adına. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">————————————————————— </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Dear list members, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">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<span> </span><b>Tue, October 15, 2024</b>. The event will be conducted online via Zoom. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The website for the event is:  <a href="https://bilecikalgebranumbertheory.github.io/" target="_blank">https://bilecikalgebranumbertheory.github.io/</a>. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The inaugural speaker will be<span> Igor Shparlinski</span>, a faculty member at University of New South Wales, Australia. Details of the presentation are provided below. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Title: </b></font><span style="color:rgb(36,41,46);font-family:monospace">Moments and non-vanishing of $L$-functions over thin subgroups</span></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Abstract: </b></font><span style="color:rgb(36,41,46);font-family:monospace">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.</span></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Date: October 15, 2024, Tuesday</font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Time: 10:00 Istanbul / 09:00 Berlin / 08:00 London </font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">To participate, simply fill out the form at the following link: </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Form Link: </font><a href="https://forms.gle/Ds3XNZXn1YNxapJU9" target="_blank">https://forms.gle/Ds3XNZXn1YNxapJU9</a></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The Zoom link will be shared via email after filling out the form. The event poster is attached. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Best regards, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Prof.Dr. Ilker Inam</font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">On behalf of the organizing committee </font></p></div></div>