BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Youness Lamzouri (Institut Élie Cartan de Lorraine\, Nancy) DTSTART;VALUE=DATE-TIME:20230111T200000Z DTEND;VALUE=DATE-TIME:20230111T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/1 DESCRIPTION:Title: Zeros of linear combinations of $L$-functions near the critical line\nby Youness Lamzouri (Institut Élie Cartan de Lorraine\, Nancy) as part of CRG Weekly Seminars\n\n\nAbstract\nIn this talk\, I will prese nt a recent joint work with Yoonbok Lee\, where we investigate the number of zeros of linear combinations of $L$-functions in the vicinity of the cr itical line. More precisely\, we let $L_1\, \\dots\, L_J$ be distinct prim itive $L$-functions belonging to a large class (which conjecturally contai ns all $L$-functions arising from automorphic representations on $\\text{G L}(n)$)\, and $b_1\, \\dots\, b_J$ be real numbers. Our main result is an asymptotic formula for the number of zeros of $F(\\sigma+it)=\\sum_{j\\leq J} b_j L_j(\\sigma+it)$ in the region $\\sigma\\geq 1/2+1/G(T)$ and $t\\i n [T\, 2T]$\, uniformly in the range $\\log \\log T \\leq G(T)\\leq (\\log T)^{\\nu}$\, where $\\nu\\asymp 1/J$. This establishes a general form of a conjecture of Hejhal in this range. The strategy of the proof relies on comparing the distribution of $F(\\sigma+it)$ to that of an associated pro babilistic random model.\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrique Treviño (Lake Forest College) DTSTART;VALUE=DATE-TIME:20230118T200000Z DTEND;VALUE=DATE-TIME:20230118T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/2 DESCRIPTION:Title: Least quadratic non-residue and related problems\nby Enriqu e Treviño (Lake Forest College) as part of CRG Weekly Seminars\n\nAbstrac t: TBA\n\nIn this talk we will talk about explicit estimates for character sums which have allowed us to find explicit estimates for the least quadr atic non-residue and other related problems.\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel R. Johnston (UNSW Canberra) DTSTART;VALUE=DATE-TIME:20230125T200000Z DTEND;VALUE=DATE-TIME:20230125T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/3 DESCRIPTION:Title: An explicit error term in the prime number theorem for large $x$\nby Daniel R. Johnston (UNSW Canberra) as part of CRG Weekly Seminar s\n\n\nAbstract\nIn 1896\, the prime number theorem was established\, show ing that $\\pi(x)\\sim \\textrm{li}(x)$. Perhaps the most widely used esti mates in explicit analytic number theory are bounds on $|\\pi(x)-\\textrm{ li}(x)|$ or the related error term $|\\theta(x)-x|$. In this talk we discu ss methods one can use to obtain good bounds on these error terms when $x$ is large. Moreover\, we will explore the many ways in which these bounds could be improved in the future.\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alisa A. Sedunova (St. Petersburg State University) DTSTART;VALUE=DATE-TIME:20230208T200000Z DTEND;VALUE=DATE-TIME:20230208T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/4 DESCRIPTION:Title: A logarithmic improvement in the Bombieri-Vinogradov theorem\nby Alisa A. Sedunova (St. Petersburg State University) as part of CRG W eekly Seminars\n\n\nAbstract\nWe improve the best known to date result of Dress-Iwaniec-Tenenbaum\, getting $(\\log{x})^2$ instead of $(\\log x)^{5/ 2}$. We use a weighted form of Vaughan's identity\, allowing a smooth trun cation inside the procedure\, and an estimate due to Barban-Vehov and Grah am related to Selberg's sieve. We give effective and non-effective version s of the result.\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Asif Zaman (University of Toronto) DTSTART;VALUE=DATE-TIME:20230215T200000Z DTEND;VALUE=DATE-TIME:20230215T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/5 DESCRIPTION:by Asif Zaman (University of Toronto) as part of CRG Weekly Se minars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ghaith Hiary (Ohio State University) DTSTART;VALUE=DATE-TIME:20230301T200000Z DTEND;VALUE=DATE-TIME:20230301T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/6 DESCRIPTION:by Ghaith Hiary (Ohio State University) as part of CRG Weekly Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Wanlin Li (Washington University in St. Louis) DTSTART;VALUE=DATE-TIME:20230201T200000Z DTEND;VALUE=DATE-TIME:20230201T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/7 DESCRIPTION:Title: The central value of Dirichlet $L$-functions over function fiel ds and related topics\nby Wanlin Li (Washington University in St. Loui s) as part of CRG Weekly Seminars\n\n\nAbstract\nA Dirichlet character ove r $\\mathbb{F}_q(t)$ corresponds to a curve over $\\mathbb{F}_q$. Using th is connection to geometry\, we construct families of characters whose $L$- functions vanish (resp. does not vanish) at the central point. The existen ce of infinitely many vanishing $L$-functions is in contrast with the situ ation over the rational numbers\, where a conjecture of Chowla predicts th ere should be no such. Towards Chowla's conjecture\, for each fixed $q$\, we present an explicit upper bound on the number of such quadratic charact ers which decreases as $q$ grows and it goes to $0$ percent as $q$ goes to infinity. In this talk\, I will also discuss phenomena and interesting qu estions related to this problem. Some results in this talk are from projec ts joint with Ravi Donepudi\, Jordan Ellenberg and Mark Shusterman.\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne-Maria Ernvall-Hytönen (University of Helsinki) DTSTART;VALUE=DATE-TIME:20230308T200000Z DTEND;VALUE=DATE-TIME:20230308T210000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/8 DESCRIPTION:by Anne-Maria Ernvall-Hytönen (University of Helsinki) as par t of CRG Weekly Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jyothsnaa Sivaraman (Chennai Mathematical Institute) DTSTART;VALUE=DATE-TIME:20230315T190000Z DTEND;VALUE=DATE-TIME:20230315T200000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/9 DESCRIPTION:by Jyothsnaa Sivaraman (Chennai Mathematical Institute) as par t of CRG Weekly Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Olga Balkanova (Steklov Mathematical Institute) DTSTART;VALUE=DATE-TIME:20230405T190000Z DTEND;VALUE=DATE-TIME:20230405T200000Z DTSTAMP;VALUE=DATE-TIME:20230208T073031Z UID:crgseminarwinter23/10 DESCRIPTION:by Olga Balkanova (Steklov Mathematical Institute) as part of CRG Weekly Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarwinter23/10/ END:VEVENT END:VCALENDAR