The distribution of values of zeta and $L$-functions

DOI10.4171/icm2022/148arXiv2112.03389OpenAlexW4389775205MaRDI QIDQ6198722

Publication date: 20 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.03389

zbMATH Keywords

moments value distribution extreme values zeta and $L$-functions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) (zeta (s)) and (L(s, chi)) (11M06) Large deviations (60F10) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Relations with random matrices (11M50)

Cites Work

Lower bounds for the maximum of the Riemann zeta function along vertical lines
Pólya-Vinogradov and the least quadratic nonresidue
Gaussian multiplicative chaos and applications: a review
GCD sums from Poisson integrals and systems of dilated functions
Maximum of the characteristic polynomial of random unitary matrices
Maxima of a randomized Riemann zeta function, and branching random walks
Large values of eigenfunctions on arithmetic hyperbolic surfaces
The fourth moment of Dirichlet $L$-functions
Large character sums: Burgess's theorem and zeros of $L$-functions
On the average of the number of imaginary quadratic fields with a given class number
The average analytic rank of elliptic curves
Moments of the Riemann zeta function
A representation theory approach to integral moments of $L$-functions over function fields
On the averages of characteristic polynomials from classical groups
A hybrid Euler-Hadamard product for the Riemann zeta function
Moments and distribution of central $L$-values of quadratic twists of elliptic curves
Extreme values of zeta and $L$-functions
The second moment of quadratic twists of modular $L$-functions
On $L$-functions of elliptic curves and cyclotomic towers
Limit theorem for the Riemann zeta-function on the critical line. II
Sur les coefficients de Fourier des formes modulaires de poids demi-entier
Values of L-series of modular forms at the center of the critical strip
Extreme values of the Riemann zeta function
The distribution of values of $L(1,\chi_d)$
The cubic moment of central values of automorphic $L$-functions
On sums of Hecke series in short intervals
On the extreme values of the Riemann zeta function on random intervals of the critical line
Extreme values of the Riemann zeta function and its argument
Sums of divisor functions in $\mathbb {F}_q[t$ and matrix integrals]
Selberg's central limit theorem for $\log|\zeta(1/2+it)|$
An effective universality theorem for the Riemann zeta function
Nonvanishing of quadratic Dirichlet $L$-functions at $s=\frac{1}{2}$
High moments of the Riemann zeta-function
Upper and lower bounds at $s=1$ for certain Dirichlet series with Euler product.
On the distribution of zeros of linear combinations of Euler products
Zeros of principal $L$-functions and random matrix theory
The sixth power moment of Dirichlet $L$-functions
The third moment of quadratic Dirichlet $L$-functions
On the maximum of the C$\beta$E field
On the third moment of $L(\frac{1}{2},\chi_d)$. II: The number field case
The fourth moment of quadratic Dirichlet $L$-functions
Moments of quadratic twists of elliptic curve $L$-functions over function fields
The Weyl bound for Dirichlet $L$-functions of cube-free conductor
The Riemann zeta function and Gaussian multiplicative chaos: statistics on the critical line
Discrepancy bounds for the distribution of the Riemann zeta-function and applications
The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture
Large greatest common divisor sums and extreme values of the Riemann zeta function
The fourth moment of quadratic Dirichlet $L$-functions over function fields
Bounding $S(t)$ and $S_1(t)$ on the Riemann hypothesis
The mean square of the product of the Riemann zeta-function with Dirichlet polynomials
Bilinear forms with Kloosterman sums and applications
The eighth moment of Dirichlet $L$-functions
Nonvanishing of Dirichlet $L$-functions
On the distribution of the values of quadratic L-series in the half-plane $\sigma > 1/2$
Twisted moments of $L$-functions and spectral reciprocity
The fifth moment of modular $L$-functions
On the moments of the moments of $(\zeta(1/2+it)$
Signs of Fourier coefficients of half-integral weight modular forms
Analytic ranks of elliptic curves over cyclotomic fields
Limit distribution of class numbers for discriminants in progressions and fundamental discriminants
Decoupling, exponential sums and the Riemann zeta function
Lower Bounds for Moments of ζ′(ρ)
The zeta function on the critical line: Numerical evidence for moments and random matrix theory models
Mod‐Gaussian convergence and the value distribution of ζ(½ + it ) and related quantities
Freezing transitions and extreme values: random matrix theory, and disordered landscapes
Mod-Gaussian convergence: new limit theorems in probability and number theory
ON THE CORRELATION OF SHIFTED VALUES OF THE RIEMANN ZETA FUNCTION
Bounding |ζ(½+it )| on the Riemann hypothesis
The distribution of the logarithm in an orthogonal and a symplectic family of L-functions
The distribution of quadratic residues and non‐residues
[https://portal.mardi4nfdi.de/wiki/Publication:3382241 The sixth moment of the Riemann zeta function and ternary additive divisor sums]
Upper bounds for moments of ζ′(ρ )
The number of imaginary quadratic fields with a given class number
The importance of the Selberg integral
The Two-Dimensional Distribution of Values of ζ(1 + it)
Explicit upper bounds for 𝐿-functions on the critical line
An arithmetical mapping and applications to Ω-results for the Riemann zeta function
Fractional Moments of the Riemann Zeta-Function
The Fourth Power Mean of Dirichlet's L-Functions
On the Mean Value of L(1/2, χ ) FW Real Characters
On a paper of Baker and Schinzel
An Improvement on a Theorem of Titchmarsh on the Mean Square of |ζ(12+it)|
THE TWELFTH POWER MOMENT OF THE RIEMANN-FUNCTION
The Fourth Power Moment of the Riemann Zeta Function
A conjecture for the sixth power moment of the Riemann zeta-function
Values of symmetric square L-functions at 1
Multiple Dirichlet Series and Moments of Zeta and L-Functions
The distribution of class numbers in a special family of real quadratic fields
The Maximum of the CUE Field
Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line
Upper Bounds for L(1, )
CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA ANDL‐FUNCTIONS
Exposé Bourbaki 1161 : The Riemann zeta function in short intervals after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan
SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION
Bagchi’s Theorem for Families of Automorphic Forms
The fifth moment of Hecke L-functions in the weight aspect
THE SUBCONVEXITY PROBLEM FOR L-FUNCTIONS
GCD sums and complete sets of square-free numbers
Upper Bounds on L-Functions at the Edge of the Critical Strip
Extreme Values of the Riemann Zeta Function on the 1-Line
MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS
Sommes de Gál et applications
Conditional bounds for the least quadratic non-residue and related problems
A note on S(t ) and the zeros of the Riemann zeta-function
Integral moments of L-functions
LARGE MOMENTS AND EXTREME VALUES OF CLASS NUMBERS OF INDEFINITE BINARY QUADRATIC FORMS
Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields
Lower bounds for moments of L -functions
The maximum size of L-functions
The Large Sieve Inequality for Algebraic Number Fields. II: Means of Moments of Hecke Zeta-Functions
Optimizing the Size of L (1, X )^†
Moments of zeta and correlations of divisor‐sums: V
The 8th Moment of the Family of $\Gamma_1(q)$-Automorphic $L$-Functions
Class numbers of indefinite binary quadratic forms
The sixth moment of automorphic $L$-functions
The non-vanishing of central values of automorphic $L$-functions and Landau-Siegel zeros
Random matrix theory and $L$-functions at $s=1/2$.
Random matrix theory and $\zeta(1/2+it)$.
A WEIGHTED CENTRAL LIMIT THEOREM FOR log|ζ(1/2+it)|
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The distribution of values of zeta and \(L\)-functions