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:20260422T230719Z UID:crgseminarfall2024/1 DESCRIPTION:Title: Explicit zero-free regions or the Riemann zeta-function for lar ge t\nby Andrew Yang (University of New South Wales Canberra\, ADFA) a s part of CRG Weekly Seminars\n\n\nAbstract\nA zero-free region of the Rie mann zeta-function is a subset of the complex plane where the zeta-functio n is known to not vanish. In this talk we will discuss various computati onal and analytic techniques used to enlarge the zero-free region for the Riemann zeta-function\, when the imaginary part of a complex zero is large . We will also explore the limitations of currently known approaches. This talk will reference a number of works from the literature\, including a j oint work with M. Mossinghoff and T. Trudgian.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine K. Chang (City University of New York) DTSTART:20241008T200000Z DTEND:20241008T210000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/2 DESCRIPTION:Title: Hybrid Statistics of the Maxima of a Random Model of the Zeta F unction over Short Intervals\nby Christine K. Chang (City University o f New York) as part of CRG Weekly Seminars\n\n\nAbstract\nWe will present a matching upper and lower bound for the right tail probability of the max imum of a random model of the Riemann zeta function over short intervals. In particular\, we show that the right tail interpolates between that of log-correlated and IID random variables as the interval varies in length. We will also discuss a new normalization for the moments over short interv als. This result follows the recent work of Arguin-Dubach-Hartung and is i nspired by a conjecture by Fyodorov-Hiary-Keating on the local maximum ove r short intervals.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Saloni Sinha (University of Missouri) DTSTART:20241015T200000Z DTEND:20241015T210000Z DTSTAMP:20260422T230719Z 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\nAbstrac t\nWe study sums of the form $\\sum_{n\\leq x} f(n) n^{-iy}$\, where $f$ i s an arithmetic function\, and we establish an equivalence between the Rie mann Hypothesis and estimates on these sums. In this talk\, we will explor e examples of such sums with specific arithmetic functions\, as well as di scuss potential implications and future research directions.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Čech (Univerzita Karlova (Charles University of Prague)) DTSTART:20241023T180000Z DTEND:20241023T190000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/4 DESCRIPTION:Title: Moments of real Dirichlet $L$-functions and multiple Dirichlet series\nby Martin Čech (Univerzita Karlova (Charles University of Pra gue)) as part of CRG Weekly Seminars\n\n\nAbstract\nThere are two ways to compute moments in families of $L$-functions: one uses the approximation b y Dirichlet polynomials\, and the other is based on multiple Dirichlet ser ies. We will introduce the two methods to study the family of real Dirichl et $L$-functions\, compare them and show that they lead to the same result s. We will then focus on obtaining the meromorphic continuation of the ass ociated multiple Dirichlet series.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Twiss (Brown University) DTSTART:20241029T200000Z DTEND:20241029T210000Z DTSTAMP:20260422T230719Z 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\nAbstrac t\nSubconvexity problems have maintained extreme interest in analytic numb er theory for decades. Critical barriers such as the convexity\, Burgess\, and Weyl bounds hold particular interest because one usually needs to dra stically 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 do not a dmit Euler products\, they are amenable to study via spectral methods. In this talk\, we construct a shifted multiple Dirichlet series (MDS) and lev erage its analytic continuation via spectral decompositions to improve upo n the Burgess bound in the conductor-aspect for the $L$-function of a holo morphic cusp form twisted by an arbitrary Dirichlet character. This improv es upon the corresponding bound obtained by Blomer-Harcos in 2008. This wo rk is joint with Jeff Hoffstein\, Nikos Diamantis\, and Min Lee.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jackie Voros (University of Bristol) DTSTART:20241105T210000Z DTEND:20241105T220000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/6 DESCRIPTION:Title: On the average least negative Hecke eigenvalue\nby Jackie V oros (University of Bristol) as part of CRG Weekly Seminars\n\n\nAbstract\ nThe least quadratic non-residue has been a central problem in number theo ry for centuries. The average least quadratic non-residue was explored by Erdős in the 1960s\, and many extensions of this problem such as to the a verage least character non-residue (Martin\, Pollack) have been explored. In this talk\, we look in to the average first sign change of Fourier coef ficients of newforms (equivalently Hecke eigenvalues). We discuss the dist ribution of Hecke eigenvalues through the so-called 'horizontal' and 'vert ical' Sato-Tate distributions\, and we also discuss large sieve inequaliti es for cusp forms that are uniform in both the weight and the level.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeriya Kovaleva (Université de Montréal) DTSTART:20241112T210000Z DTEND:20241112T220000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/7 DESCRIPTION:Title: Correlations of the Riemann Zeta on the critical line\nby V aleriya Kovaleva (Université de Montréal) as part of CRG Weekly Seminars \n\n\nAbstract\nIn this talk we will discuss the behaviour of the Riemann zeta on the critical line\, and in particular\, its correlations in variou s ranges. We will prove a new result for correlations of squares\, where s hifts 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 as the m oments of moments of the Riemann Zeta and its maximum in short intervals.\ n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Hung Bui (University of Manchester) DTSTART:20241119T210000Z DTEND:20241119T220000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/8 DESCRIPTION:Title: Mean values of Hardy's $Z$-function and weak Gram's laws\nb y Hung Bui (University of Manchester) as part of CRG Weekly Seminars\n\n\n Abstract\nWe establish the fourth moments of the real and imaginary parts of the Riemann zeta-function\, as well as the fourth power mean value of H ardy's $Z$-function at the Gram points. We also study two weak versions of Gram's law. We show that those weak Gram's laws hold a positive proportio n of time. This is joint work with Richard Hall.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicol Leong (University of New South Wales Canberra\, ADFA) DTSTART:20241126T210000Z DTEND:20241126T220000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/9 DESCRIPTION:Title: Explicit bounds for the logarithmic derivative and the reciproc al of the Riemann zeta function\nby Nicol Leong (University of New Sou th Wales Canberra\, ADFA) as part of CRG Weekly Seminars\n\n\nAbstract\nBo unds on the logarithmic derivative and the reciprocal of the Riemann zeta function are studied as they have a wide range of applications\, such as c omputing bounds for Mertens function. In this talk\, we are mainly concern ed with explicit bounds. Obtaining decent bounds are tricky\, as they 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 wi ll discuss such bounds\, their uses\, and the computational and analytic t echniques involved. Finally\, we also show how to obtain a power savings i n the case of the reciprocal of zeta.\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Chirre (Pontificia Universidad Católica del Perú) DTSTART:20240924T200000Z DTEND:20240924T210000Z DTSTAMP:20260422T230719Z UID:crgseminarfall2024/10 DESCRIPTION:Title: Remarks on a formula of Ramanujan\nby Andrés Chirre (Pont ificia Universidad Católica del Perú) as part of CRG Weekly Seminars\n\n Abstract: TBA\n LOCATION:https://researchseminars.org/talk/crgseminarfall2024/10/ END:VEVENT END:VCALENDAR