BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew Yang (University of New South Wales Canberra\, ADFA) DTSTART:20241001T200000Z DTEND:20241001T210000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/1 DESCRIPTION:Title: Explicit zero-free regions or the Riemann zeta-function for large t\nby Andrew Yang (University of New South Wales Canberra\, ADFA) as part of CRG Weekly Seminars\n\n\nAbstract\nA zero-free region of the Riemann zeta-function is a subset of the complex plane where the zeta- function is known to not vanish. In this talk we will discuss various co mputational and analytic techniques used to enlarge the zero-free region f or the Riemann zeta-function\, when the imaginary part of a complex zero i s large. We will also explore the limitations of currently known approache s. This talk will reference a number of works from the literature\, includ ing a joint work with M. Mossinghoff and T. Trudgian.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine K. Chang (City University of New York) DTSTART:20241008T200000Z DTEND:20241008T210000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/2 DESCRIPTION:Title: Hybrid Statistics of the Maxima of a Random Model of the Zeta Function over Short Intervals\nby Christine K. Chang (City Unive rsity of New York) as part of CRG Weekly Seminars\n\n\nAbstract\nWe will p resent a matching upper and lower bound for the right tail probability of the maximum of a random model of the Riemann zeta function over short inte rvals. In particular\, we show that the right tail interpolates between t hat of log-correlated and IID random variables as the interval varies in l ength. We will also discuss a new normalization for the moments over short intervals. This result follows the recent work of Arguin-Dubach-Hartung a nd is inspired by a conjecture by Fyodorov-Hiary-Keating on the local maxi mum over short intervals.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Saloni Sinha (University of Missouri) DTSTART:20241015T200000Z DTEND:20241015T210000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/3 DESCRIPTION:Title: A Study of Twisted Sums of Arithmetic Functions\nby Saloni Sinha (University of Missouri) as part of CRG Weekly Seminars\n\n\n Abstract\nWe study sums of the form $\\sum_{n\\leq x} f(n) n^{-iy}$\, wher e $f$ is an arithmetic function\, and we establish an equivalence between the Riemann Hypothesis and estimates on these sums. In this talk\, we will explore examples of such sums with specific arithmetic functions\, as wel l as discuss potential implications and future research directions.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Čech (Univerzita Karlova (Charles University of Prague)) DTSTART:20241023T180000Z DTEND:20241023T190000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/4 DESCRIPTION:Title: Moments of real Dirichlet $L$-functions and multiple Dir ichlet series\nby Martin Čech (Univerzita Karlova (Charles University of Prague)) as part of CRG Weekly Seminars\n\n\nAbstract\nThere are two w ays to compute moments in families of $L$-functions: one uses the approxim ation by Dirichlet polynomials\, and the other is based on multiple Dirich let series. We will introduce the two methods to study the family of real Dirichlet $L$-functions\, compare them and show that they lead to the same results. We will then focus on obtaining the meromorphic continuation of the associated multiple Dirichlet series.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Twiss (Brown University) DTSTART:20241029T200000Z DTEND:20241029T210000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/5 DESCRIPTION:Title: Subconvexity for $GL(2)$ $L$-functions and shifted MDS\nby Henry Twiss (Brown University) as part of CRG Weekly Seminars\n\n\n Abstract\nSubconvexity problems have maintained extreme interest in analyt ic number theory for decades. Critical barriers such as the convexity\, Bu rgess\, and Weyl bounds hold particular interest because one usually needs to drastically adjust the analytic techniques involved in order to break through them. It has recently come to light that shifted Dirichlet series can be used to obtain subconvexity results. While these Dirichlet series d o not admit Euler products\, they are amenable to study via spectral metho ds. In this talk\, we construct a shifted multiple Dirichlet series (MDS) and leverage its analytic continuation via spectral decompositions to impr ove upon the Burgess bound in the conductor-aspect for the $L$-function of a holomorphic cusp form twisted by an arbitrary Dirichlet character. This improves upon the corresponding bound obtained by Blomer-Harcos in 2008. This work is joint with Jeff Hoffstein\, Nikos Diamantis\, and Min Lee.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jackie Voros (University of Bristol) DTSTART:20241105T210000Z DTEND:20241105T220000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/6 DESCRIPTION:Title: On the average least negative Hecke eigenvalue\nby J ackie Voros (University of Bristol) as part of CRG Weekly Seminars\n\n\nAb stract\nThe least quadratic non-residue has been a central problem in numb er theory for centuries. The average least quadratic non-residue was explo red by Erdős in the 1960s\, and many extensions of this problem such as t o the average least character non-residue (Martin\, Pollack) have been exp lored. In this talk\, we look in to the average first sign change of Fouri er coefficients of newforms (equivalently Hecke eigenvalues). We discuss t he distribution of Hecke eigenvalues through the so-called 'horizontal' an d 'vertical' Sato-Tate distributions\, and we also discuss large sieve ine qualities for cusp forms that are uniform in both the weight and the level .\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeriya Kovaleva (Université de Montréal) DTSTART:20241112T210000Z DTEND:20241112T220000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/7 DESCRIPTION:Title: Correlations of the Riemann Zeta on the critical line\nby Valeriya Kovaleva (Université de Montréal) as part of CRG Weekly S eminars\n\n\nAbstract\nIn this talk we will discuss the behaviour of the R iemann zeta on the critical line\, and in particular\, its correlations in various ranges. We will prove a new result for correlations of squares\, where shifts may be up to size $T^{3/2-ε}$. We will also explain how this result relates to Motohashi’s formula for the fourth moment\, as well a s the moments of moments of the Riemann Zeta and its maximum in short inte rvals.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Hung Bui (University of Manchester) DTSTART:20241119T210000Z DTEND:20241119T220000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/8 DESCRIPTION:Title: Mean values of Hardy's $Z$-function and weak Gram's laws \nby Hung Bui (University of Manchester) as part of CRG Weekly Seminar s\n\n\nAbstract\nWe establish the fourth moments of the real and imaginary parts of the Riemann zeta-function\, as well as the fourth power mean val ue of Hardy's $Z$-function at the Gram points. We also study two weak vers ions of Gram's law. We show that those weak Gram's laws hold a positive pr oportion of time. This is joint work with Richard Hall.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicol Leong (University of New South Wales Canberra\, ADFA) DTSTART:20241126T210000Z DTEND:20241126T220000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/9 DESCRIPTION:Title: Explicit bounds for the logarithmic derivative and the r eciprocal of the Riemann zeta function\nby Nicol Leong (University of New South Wales Canberra\, ADFA) as part of CRG Weekly Seminars\n\n\nAbstr act\nBounds on the logarithmic derivative and the reciprocal of the Rieman n zeta function are studied as they have a wide range of applications\, su ch as computing bounds for Mertens function. In this talk\, we are mainly concerned with explicit bounds. Obtaining decent bounds are tricky\, as th ey are only valid in a zero-free region\, and the constants involved tend to blow up as one approaches the edge of the region\, and a potential zero . We will discuss such bounds\, their uses\, and the computational and ana lytic techniques involved. Finally\, we also show how to obtain a power sa vings in the case of the reciprocal of zeta.\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Chirre (Pontificia Universidad Católica del Perú) DTSTART:20240924T200000Z DTEND:20240924T210000Z DTSTAMP:20260404T095029Z UID:crgseminarfall2024/10 DESCRIPTION:Title: Remarks on a formula of Ramanujan\nby Andrés Chirr e (Pontificia Universidad Católica del Perú) as part of CRG Weekly Semin ars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/crgseminarfall2024/10/ END:VEVENT END:VCALENDAR