The Relative Trace Formula in Analytic Number Theory
DOI10.1007/978-3-030-68506-5_2zbMath1483.11101arXiv1912.08137OpenAlexW2996617194MaRDI QIDQ4956856
Publication date: 2 September 2021
Published in: Simons Symposia (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.08137
\(L\)-functionsequidistributionmodular grouptrace formulaKloosterman sumscusp formsFourier coefficientKuznetsov formulaBruggeman formula
Modular and automorphic functions (11F03) Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the 4-norm of an automorphic form
- A Sato-Tate law for \(\mathrm{GL}(3)\)
- A family of Calabi-Yau varieties and potential automorphy. II.
- Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
- Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
- Distribution of periodic torus orbits and Duke's theorem for cubic fields
- Théorème de Brun-Titchmarsh; application au théorème de Fermat
- On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
- The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points. II
- The quantum unique ergodicity conjecture for thin sets
- On the Kuznetsov-Bruggeman formula for a Hilbert modular surface having one cusp
- Trilinear forms and the central values of triple product \(L\)-functions
- Twisted \(L\)-functions over number fields and Hilbert's eleventh problem
- Primes in arithmetic progressions to large moduli
- Poincaré series on \(\mathrm{GL}(r)\) and Kloosterman sums
- Fourier coefficients of modular forms of half-integral weight
- Poincaré series for GL(n): Fourier expansion, Kloosterman sums, and algebreo-geometric estimates
- Hyperbolic distribution problems and half-integral weight Maass forms
- On the greatest prime factor of \((n^2)+1\)
- Kloosterman sums and Fourier coefficients of cusp forms
- Fourier coefficients of cusp forms
- The behaviour of eigenstates of arithmetic hyperbolic manifolds
- The cubic moment of central values of automorphic \(L\)-functions
- The \(L^2\) restriction norm of a Maass form on \(\mathrm{SL}_{n+1}(\mathbb {Z})\)
- Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms
- The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points
- Equidistribution of roots of a quadratic congruence to prime moduli
- Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
- Global decomposition of \(\operatorname{GL}(3)\) Kloosterman sums and the spectral large sieve
- Distribution of Maass of holomorphic cusp forms
- Refined global Gross-Prasad conjecture on special Bessel periods and Böcherer's conjecture
- On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture
- The arithmetic Kuznetsov formula on \(\mathrm{GL}(3)\). I: The Whittaker case
- A spectral reciprocity formula and non-vanishing for \(L\)-functions on \(\mathrm{GL}(4)\times\mathrm{GL}(2)\)
- Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\). II: The level aspect
- Spectral summation formula for GSp(4) and moments of spinor \(L\)-functions
- Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\)
- Uniform bound for Hecke \(L\)-functions
- \(L^4\)-norms of Hecke newforms of large level
- Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties
- Weyl-type hybrid subconvexity bounds for twisted \(L\)-functions and Heegner points on shrinking sets
- The Spectral Kuznetsov Formula on $SL(3)$
- Subconvexity and equidistribution of Heegner points in the level aspect
- The L2 restriction norm of a GL3 Maass form
- On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
- Subconvexity for twisted <i>L</i>-functions on GL(3)
- On the subconvexity problem for L-functions on GL(3)
- Poincaré series and Kloosterman sums for SL(3, Z)
- More than two fifths of the zeros of the Riemann zeta function are on the critical line.
- PETERSSON'S CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK'S CONJECTURE. SUMS OF KLOOSTERMAN SUMS
- Regular and irregular semiclassical wavefunctions
- Beyond Endoscopy and special forms on GL(2)
- The prime geodesic theorem
- Plancherel Distribution of Satake Parameters of Maass Cusp Forms on GL3
- On the fourth moment of Hecke–Maass forms and the random wave conjecture
- An orthogonality relation for (with an appendix by Bingrong Huang)
- MOMENTS OF SPINOR L-FUNCTIONS AND SYMPLECTIC KLOOSTERMAN SUMS
- Beyond Endoscopy via the trace formula, II: Asymptotic expansions of Fourier transforms and bounds towards the Ramanujan conjecture
- Local spectral equidistribution for Siegel modular forms and applications
- Bounds for modular L-functions in the level aspect☆
- Automorphic Forms and L-Functions for the GroupGL(n, R)
- On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions
- Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
- Low-lying zeros of families of elliptic curves
- On Some Exponential Sums
- SOME EIGENFUNCTION FORMULAE
- The first case of Fermat's last theorem
- Fourier coefficients of Siegel cusp forms of degree two
- Number Theory
- A Kuznetsov formula for Kloosterman sums on \(\text{GL}_n\)
- Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity
- Low lying zeros of families of \(L\)-functions
- Nonvanishing of \(L\)-values and the Weyl law
- Quantum unique ergodicity for \(\text{SL}_2 (\mathcal O)\backslash\mathbb{H}^3\) and estimates for \(L\)-functions
This page was built for publication: The Relative Trace Formula in Analytic Number Theory