This is the webpage for the grad seminar of the focused research group on averages of \(L\)-functions and arithmetic stratification funded by the NSF grant DMS-1854398, centered at the American Institute of Mathematics.

This is an online seminar aimed at early career researchers in the FRG, though senior researchers often attend.

If you would like to volunteer to give a talk, or you would like to attend the seminar, please send me an email.

For the past and future schedule, please see below. For the notes and recordings of past talks, please see the sidebar.

Final Talk [29-Apr-2024]

Brian Conrey (AIM)

Averages of L-functions and arithmetic stratification: a report on the FRG

Abstract: I will give an update on some of the work that has been done since the FRG started.

Past Talks

Spring 2024

[22-Apr-2024] Problem Session

Moderator: Ofir Gorodetsky (problem list)

[16-Apr-2024] Jonathan Keating (Oxford)

“Joint Moments” (notes, video)

[09-Apr-2024] Steve Gonek (Rochester)

“Universality of \(L\)-Functions over finite function fields” (video)

[01-Apr-2024] Ertan Elma (Lethbridge)

“A discrete mean value of the Riemann zeta function and its derivatives” (notes, video)

[25-Mar-2024] Quanli Shen (Shandong, Weihai)

“The fourth moment of quadratic Dirichlet L-functions II” (notes, video)

[18-Mar-2024] Prahlad Sharma (MPIM)

“Counting special points on quadratic surfaces” (notes, video)

[04-Mar-2024] Seth Hardy (Warwick)

“Bounds for exponential sums with random multiplicative coefficients” (notes, video)

[26-Feb-2024] Vivian Kuperberg (ETH Zürich)

“Sums of odd-ly many fractions” (notes, video)

[19-Feb-2024] Jackie Voros (Bristol)

“On the average least negative Hecke eigenvalue” (video)

[12-Feb-2024] Alexandre de Faveri (Stanford)

“An inequality for GL(3) Fourier coefficients” (notes, video)

[05-Feb-2024] Siegfred Baluyot (AIM)

“Twisted moments of characteristic polynomials of random matrices” (video)

[29-Jan-2024] Trevor Wooley (Purdue)

“Primes as sums of k-th powers, and Freiman's theorem” (video)

Fall 2023

[18-Dec-2023] Maxim Gerspach (KTH)

“Heuristics and random models for quadratic character sums” (notes, video)

[11-Dec-2023] Andrés Chirre (PUCP Lima)

“Remarks on a formula of Ramanujan” (notes, video)

[27-Nov-2023] Michael Yiasemides (LSE)

“Lattice Points in Function Fields, and Hankel Matrices” (notes, video)

[20-Nov-2023] Steve Lester (KCL)

“Around the Gauss circle problem” (notes, video)

[13-Nov-2023] Julia Stadlmann (Oxford)

“Primes in arithmetic progressions to smooth moduli” (notes, video)

[06-Nov-2023] Michael Curran (Oxford)

“Correlations of the Riemann zeta function” (notes, video)

[30-Oct-2023] Sacha Mangerel (Durham)

“Large order Dirichlet characters and an analogue of a conjecture of Vinogradov” (notes, video)

[23-Oct-2023] Winston Heap (NTNU)

“Simultaneous extreme values of zeta and L-functions” (notes, video)

[02-Oct-2023] Agniva Dasgupta (Texas A&M)

“Short Second Moment Bound for GL(2) L-functions in the Level Aspect” (notes, video)

[25-Sep-2023] Henryk Iwaniec (Rutgers)

“Integer Parts Mutually Coprime” (notes)

[18-Sep-2023] Mayank Pandey (Princeton)

“\(L^1\) means of exponential sums with multiplicative coefficients” (video)

Spring 2023

[05-Jun-2023] Emily Quesada-Herrera (TU Graz)

“On the vertical distribution of the zeros of the Riemann zeta-function” (notes, video)

[29-May-2023] Jaime Hernandez Palacios (Mississippi)

“Gaps between zeros of zeta and L-functions of high degree” (notes)

[22-May-2023] Igor Shparlinski (UNSW)

“Bilinear forms with Kloosterman and Salié Sums and Moments of L-functions” (notes, video)

[15-May-2023] Vorappan (Fai) Chandee (Kansas State)

“The eighth moment of \(\Gamma_1(q)\) L-functions” (notes, video)

[08-May-2023] Alessandro Fazzari (AIM)

“Averages of long Dirichlet polynomials with modular coefficients” (notes, video)

[01-May-2023] Kiseok Yeon (Purdue)

“The Hasse principle for random projective hypersurfaces via the circle method” (notes, video)

[24-Apr-2023] Eun Hye Lee (Stony Brook)

“The Shintani Zeta Functions” (notes, video)

[17-Apr-2023] Matilde Lalín (Montréal)

“The distribution of values of cubic \(L\)-functions at \(s=1\)” (notes, video)

[10-Apr-2023] Aleksander Simonič (UNSW Canberra)

“Some conditional estimates for functions in the Selberg class” (notes, video)

[20-Mar-2023] Peter Zenz (Brown)

“On the Distribution of Holomorphic Cusp Forms and Applications” (notes, video)

[13-Mar-2023] Ian Whitehead (Swarthmore)

“Multiple Dirichlet Series and Moments of L-functions” (video)

[10-Mar-2023] Ofir Gorodetsky (Oxford)

“How many smooth numbers and smooth polynomials are there?” (notes, video)

[27-Feb-2023] Xiannan Li (Kansas State)

“Quadratic Twists of Modular L-functions” (notes, video)

[20-Feb-2023] Katy Woo (Princeton)

“Small scale distribution of primes in four-term arithmetic progressions” (notes, video)

[13-Feb-2023] Rizwanur Khan (Mississippi)

“The fourth moment of Dirichlet L-functions and related problems” (notes, video)

[06-Feb-2023] Keshav Aggarwal (Rényi Institute)

“Bound for the existence of prime gap graphs” (notes, video)

[30-Jan-2023] David Farmer (AIM)

“The zeta function when it is particularly large” (notes, video)

[23-Jan-2023] Nathan Ng (Lethbridge)

“The eighth moment of the Riemann zeta function” (notes, video)

Fall 2022

[19-Dec-2022] George Dickinson (Manchester)

“Second moments of Dirichlet L-functions” (notes, video)

[12-Dec-2022] Alexander Dobner (Michigan)

“Optimization and moment methods in number theory” (notes, video)

[05-Dec-2022] Asif Zaman (Toronto)

“Random multiplicative functions and a simplified model”

[28-Nov-2022] Aled Walker (KCL)

“Correlations of sieve weights and distributions of zeros” (notes, video)

[21-Nov-2022] Alexander Dunn (Caltech)

“Bias in cubic Gauss sums: Patterson's conjecture” (video)

[14-Nov-2022] Jakob Streipel (Maine)

“Using second moments to count zeros” (notes, video)

[07-Nov-2022] Daodao Yang (TU Graz)

“Large values of derivatives of the Riemann zeta function and related problems” (notes)

[31-Oct-2022] Emma Bailey (CUNY)

“Large values of \(\zeta\) on the critical line” (video)

[17-Oct-2022] Dan Goldston (SJSU)

“Small gaps and spacings between Riemann zeta-function zeros” (notes, video)

[10-Oct-2022] Lasse Grimmelt (Oxford)

“Primes in large arithmetic progressions and applications to additive problems” (notes, video)

[03-Oct-2022] Louis Gaudet (Rutgers)

“The least Euler prime via a sieve approach” (video)

[26-Sep-2022] Hua Lin (UC Irvine)

“One-level density of zeros of Dirichlet L-function over function fields” (notes, video)

[22-Sep-2022] Caroline Turnage-Butterbaugh (Carleton)

“Moments of Dirichlet L-functions” (notes)

Spring 2022

[30-May-2022] Micah Milinovich (Mississippi)

“Estimates for zeta and L-functions via Fourier optimization” (notes, video)

[23-May-2022] Jori Merikoski (Oxford)

“Primes in sparse polynomials sets” (notes, video)

[16-May-2022] Martin Čech (Concordia)

“Two ways to compute moments in the family of real Dirichlet L-functions” (notes, video)

[02-May-2022] Alexandra Florea (UC Irvine)

“Upper bounds for positive and negative moments of the Riemann zeta function” (notes, video)

[25-Apr-2022] Kevin Hughes (Bristol)

“A primer on Discrete Restriction Theory” (notes, video)

[18-Apr-2022] Alia Hamieh (UNBC)

“Distribution of values of logarithmic derivatives of L-functions” (notes, video)

[11-Apr-2022] Ayla Gafni (Mississippi)

“Uniform distribution and geometric incidence theory” (video)

[04-Apr-2022] Victor Wang (Princeton)

“Special subvarieties over finite and infinite fields” (notes, video)

[28-Mar-2022] Joshua Stucky (Kansas State)

“Smooth numbers in arithmetic progressions” (notes, video)

[21-Mar-2022] Kunjakanan Nath (UIUC)

“Primes with restricted digits” (notes, video)

[14-Mar-2022] Ofir Gorodetsky (Oxford)

“Chebyshev's bias for primes and for sums of two squares” (notes, video)

[07-Mar-2022] Vivian Kuperberg (Stanford)

“The Hardy–Littlewood \(k\)-tuple conjecture and intervals with many primes” (notes, video)

[28-Feb-2022] Peter Humphries (Virginia)

“Spectral reciprocity and applications” (notes, video)

[14-Feb-2022] Siegfred Baluyot (AIM)

“The shifted convolution of divisor functions” (notes, video)

Fall 2021

[13-Dec-2021] Brad Rodgers (Queen's)

“Averages of products and ratios of L-functions and characteristic polynomials” (video)

[29-Nov-2021] Chung-Hang (Kevin) Kwan (Columbia)

“Some aspects of \(\Gamma\)-functions” (notes, video)

[22-Nov-2021] Fan Ge (William & Mary)

“Critical points of the Riemann zeta-function” (notes, video)

[15-Nov-2021] Fatma Çiçek (IIT Gandhinagar)

“Value distribution of the Riemann zeta-function on the half-line” (notes, video)

[08-Nov-2021] Emilia Alvarez (Bristol)

“Random matrices and Painlevé equations” (video)

[02-Nov-2021] Shehzad Hathi (UNSW Canberra)

“The LLL algorithm and its applications to Mertens conjecture” (notes, video)

[25-Oct-2021] Max Wenqiang Xu (Stanford)

“Limiting distributions of sums of random multiplicative functions” (notes, video)

[11-Oct-2021] Louis Gaudet (Rutgers)

“The Kloosterman Circle Method” (notes, video)

[04-Oct-2021] Caroline Turnage-Butterbaugh (Carleton)

“Gaps between zeros of the Riemann zeta-function” (notes, video)

Spring 2021

[21-Jun-2021] Akshat Mudgal (Bristol/Purdue)

“An introduction to Vinogradov’s mean value theorem” (notes, video)

[14-Jun-2021] Amita Malik (AIM/MPIM)

“Equidistribution of \(\alpha p^{\theta}\) with a Chebotarev condition and applications to extremal primes” (video)

[07-Jun-2021] Winston Heap (Shandong)

“Mean values of long Euler products” (notes, video)

[17-May-2021] Jared Duker Lichtman (Oxford)

“The Riemann hypothesis for curves” (notes, video)

[19-Apr-2021] Vivian Kuperberg (Stanford)

“The second moment of quadratic twists of modular L-functions (after Soundararajan and Young)” (notes, video)

[12-Apr-2021] Ofir Gorodetsky (Oxford)

“The variance of the sum of an arithmetic function over random short intervals” (notes, video)

[08-Mar-2021] Max Wenqiang Xu (Stanford)

“Distribution and moments of random multiplicative functions” (notes, video)

[22-Feb-2021] Chung-Hang (Kevin) Kwan (Columbia)

“Averages of Fourier coefficients” (notes, video)

[15-Feb-2021] Quanli Shen (Lethbridge)

“The first moment of quadratic twists of modular L-functions” (notes, video)

[08-Feb-2021] Emilia Alvarez (Bristol)

“An overview of random matrix theory for number theorists” (notes, video)

[01-Feb-2021] Alessandro Fazzari (Genova)

“A survey on the central limit theorem for the Riemann zeta function” (notes, video)