Number theory
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2332 Artin’s Primitive-Root Density for Two
- Math-2333 Primitive-Root Density Formulas for Rank-One Tori
- Math-2334 Parity Conjectures for Elliptic Curves over Number Fields
- Math-2338 Exponential Distribution of Normalized Prime Gaps
- Math-2343 Local $p$-Adic Section Conjecture
- Math-2346 Parity of 2-Primary Tate–Shafarevich Groups
- Math-2347 Section Conjecture for Hyperbolic Curves Without Boundary Points
- Math-2348 Section Conjecture for Hyperbolic Curves
- Math-2406 The mod-$\ell$ Bogomolov–Pop conjecture
- Math-2436 Generalized Riemann Hypothesis for Automorphic L-Functions
- Math-2444 Rank-One Equivalences for Elliptic Curves
- Math-2474 Spectral-Deformation Methods for the Riemann Hypothesis
- Math-2475 Zilber-Pink Unlikely Intersection Conjecture
- Math-2496 Arthur-Langlands Reciprocity
- Math-2500 Maximum Normalized Mahler Measure of Littlewood Polynomials
- Math-2502 Rank Distribution in Quadratic-Twist Families
- Math-2770 Elliptic-square intersections of Hodge-generic curves in A2
- Math-2771 Product-CM intersections of Hodge-generic curves in A2
- Math-2772 Quaternionic division intersections of Hodge-generic curves in A2
- Math-2773 Zilber-Pink for abelian varieties over Qbar
- Math-2774 Primitive-root infinitude for every admissible base
- Math-2775 Corrected binary Elliott for ordinary averages
- Math-2776 Integral-point density on curve character varieties
- Math-2777 The exact BSD formula at low Selmer corank
- Math-2778 Generic Ramanujan for exceptional groups over function fields
- Math-2779 An explicit asymptotic formula for the number of totients
- Math-2780 Odd regular Fontaine-Mazur over Q at two
- Math-2781 Full finite-level Ramanujan-Arthur decomposition
- Math-2782 Global Arthur enhancements of occurring excursion parameters
- Math-2783 Goldfeld analytic rank density over Q
- Math-2784 Mean analytic rank of quadratic twists over Q
- Math-2785 Modularity of elliptic curves over imaginary quadratic fields
- Math-2786 The joint Dickman law for consecutive integers
- Math-2787 Milnor K reconstruction at the characteristic prime
- Math-2788 Tame eigensheaves at several marked points
- Math-2789 Ordinary binary affine Liouville correlations
- Math-2790 Additive indecomposability of finite modifications of the primes
- Math-2791 Patterson first moment over Eisenstein primes
- Math-2792 Positive lower density of arbitrarily large normalized prime gaps
- Math-2793 Power-free values of irreducible polynomials of degrees four to eight
- Math-2794 Prime predecessors with even squarefree factor count
- Math-2795 Poisson-Dirichlet factorization of prime predecessors
- Math-2796 Bogomolov-Pop pro-ell reconstruction
- Math-2797 The eleven-twelfths zero-free half-plane
- Math-2798 The seven-eighths zero-free half-plane
- Math-2799 Rationality of the canonical unramified Arthur filtration
- Math-2800 Constructible tame eigensheaves with regular monodromy
- Math-2801 Restricted geometric Langlands in the stated positive-characteristic regimes
- Math-2802 Many primes with power-smooth predecessors
- Math-2803 Open homomorphisms of solvably closed global Galois groups