Low lying zeros of families of \(L\)-functions

From MaRDI portal

Publication:5945310

Jump to:navigation, search

DOI10.1007/BF02698741zbMath1012.11041arXivmath/9901141WikidataQ101221017 ScholiaQ101221017MaRDI QIDQ5945310

Peter C. Sarnak, Henryk Iwaniec, Wenzhi Luo

Publication date: 18 June 2002

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9901141

zbMATH Keywords

zeros automorphic \(L\)-functions lower estimates central values random matrix model density theorems frequency of nonvanishing Hecke \(L\)-functions quasi-Riemann hypothesis symmetric square \(L\)-functions

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items

Sums of Fourier coefficients of cusp forms of level \(D\) twisted by exponential functions, LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE -FUNCTIONS, Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions, Average values of symmetric square $L$-functions at the edge of the critical strip, Subconvexity bounds for twisted 𝐿-functions, II, Omega results for cubic field counts via lower-order terms in the one-level density, Analytic isolation of newforms of given level, Applications of theL-functions ratios conjectures, AVERAGES OF EXPONENTIAL TWISTS OF THE VON MANGOLDT FUNCTION, Fourier coefficients at primes twisted with exponential functions, Low-lying zeros of cubic Dirichlet \(L\)-functions and the ratios conjecture, An omega result for supremum norms of Hecke-eigenforms in the level aspect, Sato-Tate theorem for families and low-lying zeros of automorphic \(L\)-functions. Appendix A by Robert Kottwitz, and Appendix B by Raf Cluckers, Julia Gordon and Immanuel Halupczok., Symplectic n-level densities with restricted support, ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS, Petersson products of bases of spaces of cusp forms and estimates for Fourier coefficients, The third-power moment of the Riesz mean error term of symmetric square \(L\)-function, Sub-convexity bound for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions: the depth aspect, On Montgomery's pair correlation conjecture: a tale of three integrals, Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble, AVERAGES OF TWISTED -FUNCTIONS, One-level density estimates for Dirichlet \(L\)-functions with extended support, Lower-Order Biases in the Second Moment of Dirichlet Coefficients in Families of L-Functions, Bounds for average toward the resonance barrier for \(\mathrm{GL}(3) \times\mathrm{GL}(2)\) automorphic forms, Averages of long Dirichlet polynomials with modular coefficients, A weighted one-level density of families of \(L\)-functions, The cubic Pell equation $L$-function, Fourier coefficients of automorphic L-functions, Analytic twists of GL2×GL2$\rm GL_2\times \rm GL_2$ automorphic forms, Analytic number theory. Abstracts from the workshop held November 6--12, 2022, Distribution of Hecke Eigenvalues for GL(n), Some Results in the Theory of Low-Lying Zeros of Families of L-Functions, Families of L-Functions and Their Symmetry, Double square moments and bounds for resonance sums of cusp forms, Selberg's central limit theorem for quadratic Dirichlet \(L\)-functions over function fields, One-level density of quadratic twists of $L$-functions, Extreme values of L$L$‐functions of newforms, The average of the exponential sums related to cusp forms, The metric theory of the pair correlation function for small non‐integer powers, Kloosterman sums do not correlate with periodic functions, Determining optimal test functions for 2-level densities, Jacobi forms, Saito-Kurokawa lifts, their pullbacks and sup-norms on average, LOW‐LYING ZEROS OF L ‐FUNCTIONS FOR MAASS FORMS OVER IMAGINARY QUADRATIC FIELDS, The fourth moment of Dirichlet \(L\)-functions along a coset and the Weyl bound, Analytic ranks of automorphic L$L$‐functions and Landau–Siegel zeros, The fifth moment of Hecke L-functions in the weight aspect, First moment of Rankin-Selberg central \(L\)-values and subconvexity in the level aspect, Unnamed Item, Weighted Distribution of Low-lying Zeros of GL(2) -functions, Extremal functions in de Branges and Euclidean spaces, A density theorem on automorphic $L$-functions and some applications, Low-lying zeros of families of elliptic curves, Local spectral equidistribution for Siegel modular forms and applications, Explicit formulas for the spectral side of the trace formula of ${\rm SL(2)}$, The smallest prime in a conjugacy class and the first sign change for automorphic 𝐿-functions, Orthogonal and symplectic 𝑛-level densities, Bias of root numbers for modular newforms of cubic level, On a sum involving Fourier coefficients of cusp forms, Quantum variance for Hecke eigenforms☆, Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity, On the first sign change of Hecke eigenvalues of newforms, Real zeros and size of Rankin-Selberg \(L\)-functions in the level aspect, On modular signs, Algebraic trace functions over the primes, Maass Waveforms and Low-Lying Zeros, Resonance sums for Rankin-Selberg products of \(\mathrm{SL}_m(\mathbb{Z})\) Maass cusp forms, The Relative Trace Formula in Analytic Number Theory, \(L^4\)-norms of Hecke newforms of large level, Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique, Generalized Riemann hypothesis and stochastic time series, One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke -functions, On the fourth moment of Hecke–Maass forms and the random wave conjecture, Super-positivity of a family of L-functions, Kuznetsov’s trace formula and the Hecke eigenvalues of Maass forms, From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, Resonance of automorphic forms for 𝐺𝐿(3), Subconvexity for twisted 𝐿-functions on 𝐺𝐿₃ over the Gaussian number field, Non-vanishing of derivatives of 𝐺𝐿(3)×𝐺𝐿(2) 𝐿-functions, Average values of symmetric square \(L\)-functions at the edge of the critical strip, Local spectral equidistribution for degree two Siegel modular forms in level and weight aspects, Generalized Riemann hypothesis, time series and normal distributions, Zeroes of zeta functions and symmetry, A case of simultaneous non-vanishing of automorphic $L$-functions, Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis, The second moment of twisted modular \(L\)-functions, Motohashi’s formula for the fourth moment of individual DirichletL-functions and applications, \(L^4\)-norms of the holomorphic dihedral forms of large level, Sums of Fourier coefficients of cusp forms of level 𝐷 twisted by exponential functions over arithmetic progressions, Low-lying zeros of quadratic Dirichlet -functions: lower order terms for extended support, Low-lying zeros of dihedral \(L\)-functions, Distribution of values of symmetric power \(L\)-functions at the edge of the critical strip, On exponential sums involving Fourier coefficients of cusp forms over primes, Density theorems for exceptional eigenvalues for congruence subgroups, An exponential sum involving Fourier coefficients of eigenforms for \(\mathrm{SL}(2,\mathbb{Z})\), Hybrid subconvexity bounds for \(L \left( \frac{1}{2}, \mathrm{Sym}^2 f \otimes g\right) \), Rankin-Selberg \(L\)-functions and the reduction of CM elliptic curves, \(n\)-level densities for twisted cubic Dirichlet \(L\)-functions, Averages of central \(L\)-values of Hilbert modular forms with an application to subconvexity, Arithmetic statistics of modular symbols, Oscillations of Hecke eigenvalues at shifted primes, The volumes of Miyauchi subgroups, Estimates for Fourier coefficients of cusp forms in weight aspect, Moments of \(S(t,f)\) associated with holomorphic Hecke cusp forms, Low-lying zeros of \(L\)-functions with orthogonal symmetry, Optimal test functions for detecting central point vanishing over families of \(L\)-functions, Pair correlation of zeros of \(\Gamma_1(q)\) L-functions, Weighted one-level density of low-lying zeros of Dirichlet \(L\)-functions, One-level density of the family of twists of an elliptic curve over function fields, On the 4-norm of an automorphic form, Non-linear additive twists of \(\operatorname{GL}(3) \times \operatorname{GL}(2)\) and \(\operatorname{GL}(3)\) Maass forms, Values of automorphic \(L\)-functions with prime power level at the point \(s=1\), On the estimation of nonlinear twists of the Liouville function, Exponential sums formed with the von Mangoldt function and Fourier coefficients of \(\mathrm{GL}(m)\) automorphic forms, The first moment of \(L\)-functions of primitive forms on \(\Gamma _{0}(p^\alpha )\) and a basis of old forms, Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for \(\mathrm{GL}_m(\mathbb Z)\), Newman's conjecture in various settings, Spectral square moments of a resonance sum for Maass forms, Resonance between automorphic forms and exponential functions, The second moment of \(\text{GL}(3)\times\text{GL}(2)\) \(L\)-functions, integrated, Zeroes of quaternionic modular forms and central \(L\)-values, Double square moments and subconvexity bounds for Rankin-Selberg \(L\)-functions of holomorphic cusp forms, Asymptotic trace formula for the Hecke operators, Refined dimensions of cusp forms, and equidistribution and bias of signs, Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions, Low-lying zeros of number field \(L\)-functions, Type-I contributions to the one and two level densities of quadratic Dirichlet \(L\)-functions over function fields, Lower order terms for the one-level density of a symplectic family of Hecke \(L\)-functions, Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field, Special values of symmetric power \(L\)-functions and Hecke eigenvalues, Exponential sums involving automorphic forms for \(\mathrm{GL}(3)\) over arithmetic progressions, The analytic rank of \(J_0(q)\) and zeros of automorphic \(L\)-functions., On the distribution of Hecke eigenvalues over Piatetski-Shapiro prime twins, The horocycle flow at prime times, A generalized cubic moment and the Petersson formula for newforms, A twisted Motohashi formula and Weyl-subconvexity for \(L\)-functions of weight two cusp forms, Estimates of a certain sum involving coefficients of cusp forms in weight and level aspects, Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\), On the low-lying zeros of Hasse-Weil \(L\)-functions for elliptic curves, Oscillations of Fourier coefficients of \(\mathrm{GL}(m)\) Hecke-Maass forms and nonlinear exponential functions at primes, One-level density of families of elliptic curves and the Ratios Conjecture, One-level density for holomorphic cusp forms of arbitrary level, Hybrid bounds for Rankin-Selberg \(L\)-functions, Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function, Special value formula for the twisted triple product \(L\)-function and an application to the restricted \(L^2\)-norm problem, An elliptic curve test of the \(L\)-functions ratios conjecture, On the effective determination of Maass cusp forms by \(L\)-values, Additive twists of Fourier coefficients of modular forms, Non-vanishing of \(L\)-functions of Hilbert modular forms at the central point, Nonlinear exponential twists of the Liouville function, Exponential sums involving Maass forms, Oscillations of cusp form coefficients over primes, Small first zeros of \(L\)-functions, The average analytic rank of elliptic curves, A unitary test of the Ratios Conjecture, Determining cusp forms by central values of Rankin-Selberg \(L\)-functions, Twisted moments of automorphic \(L\)-functions, \(L\)-functions of automorphic forms and combinatorics: Dyck paths., Oscillations of cusp form coefficients in exponential sums, Spectral asymptotics for arithmetic quotients of \(\text{SL}(n,{\mathbb R})/\text{SO}(n)\), Kloosterman sums in residue classes, Quantum variance of Maass-Hecke cusp forms, On Fourier coefficients of modular forms of half integral weight at squarefree integers, Twisted \(L\)-functions over number fields and Hilbert's eleventh problem, Asymptotic properties of Dedekind zeta functions in families of number fields, On tensor product \(L\)-functions for quaternion unitary groups and \(\mathrm{GL}(2)\) over totally real number fields: mixed weight cases, More than five-twelfths of the zeros of \(\zeta\) are on the critical line, Moments of \(L\)-functions and the Liouville-Green method, Computing the Laplace eigenvalue and level of Maass cusp forms, Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families, Non-vanishing of the derivative of \(L\)-functions at the central point, Brauer-Siegel theorem for families of elliptic surfaces over finite fields, Applications of analytic newvectors for \(\operatorname{GL}(N)\), Dirichlet characters and low-lying zeros of \(L\)-functions, On the random wave conjecture for dihedral Maaß forms, Lower order terms for the one-level density of elliptic curve \(L\)-functions, Equidistribution of Fourier coefficients of square and cube symmetric \(L\)-functions, Oscillations of coefficients of primitive cusp forms over some special sequences, Some remarks on Landau-Siegel zeros, Rankin-Selberg \(L\)-functions in the level aspect., Low lying zeros of Artin \(L\)-functions, Hilbert spaces and low-lying zeros of \(L\)-functions, Resonances and \(\Omega\)-results for exponential sums related to Maass forms for \(\mathrm{SL}(n, \mathbb{Z})\), Bias of root numbers for Hilbert newforms of cubic level, Equidistribution of Hecke eigenforms on the arithmetic surface \(\Gamma_0(N)\setminus {\mathbb H}\)., Bounding vanishing at the central point of cuspidal newforms, Low-lying zeros of \(L\)-functions for quaternion algebras, Bounds toward hypothesis S for cusp forms, Hybrid subconvexity bounds for \(L(1/2,\operatorname{sym}^2 f \otimes \chi)\), A local large sieve inequality for cusp forms

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:5945310&oldid=12103126"