Open Research Index

871 records

  1. Iwaniec's linear sieve at the sifting limit and Jacobsthal's problem

    Jason Davies

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  2. Sums of primes, after Hardy and Littlewood 1923, Partitio Numerorum III, Theorems B to F proved without Hypothesis R

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  3. Conditional on RH: the Cesàro average of the number of Goldbach representations, after Goldston and Yang

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  4. Mann's alpha plus beta theorem for Schnirelmann density, after Mann 1942

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  5. Conditional on RH: the number of Goldbach representations on average, after Languasco and Zaccagnini

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  6. The Bombieri-Vinogradov theorem, Bombieri 1965 and A. I. Vinogradov 1965, classical form with the maximum over y <= x

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  7. Noncrossing Two-Nearest-Predecessor Orders on Nearly Circular Ellipses

    John Fairfax-Ball

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  8. Renyi's theorem, Renyi 1948: every large even number is a prime plus a number with at most 8 prime factors

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  9. Szemerédi's theorem with random differences

    Gabriel Dahia

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  10. The least physical dimension of an inflation-symmetric model set, with the cubic, quartic and degree-12 inflations of x^3 - x - 1 and x^4 - x - 1

    Stephanie Alexander

    Palomar RegistryOct 22, 2026math.MGmachine-checkedscore 0

  11. Sum of sets in several dimensions

    Gabriel Dahia

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  12. An exact average Goldbach representation formula, after Goldston and Suriajaya

    Steve Hubbard

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  13. Helling's theorem: the maximal subgroups of SL₂(ℝ) commensurable with SL₂(ℤ)

    Filip Najman

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  14. Continuous open images of Polish spaces

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 22, 2026math.GNmachine-checkedscore 0

  15. The expander mixing lemma and the Alon–Boppana bound

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  16. Cubic-rate irrationality for reciprocal sums

    Will Cook

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  17. Uniform sparse rationalisation of dyadic series

    Will Cook

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  18. Infinite rank of the three-prime running-LCM kernel

    Will Cook

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  19. An explicit rational-base irrationality region for Zudilin's Lambert series

    Will Cook

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  20. Carry and divisor-channel criteria for the factorial-minus-one reciprocal series

    Will Cook

    Palomar RegistryOct 22, 2026math.NTmachine-checkedscore 0

  21. Open Baire-space representation of Polish spaces

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 22, 2026math.GNmachine-checkedscore 0

  22. Alexandrov–Urysohn characterization of Baire space

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 22, 2026math.GNmachine-checkedscore 0

  23. The Bondy–Simonovits even cycle theorem

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 22, 2026math.COmachine-checkedscore 0

  24. Jaeger's 4-flow and 8-flow theorems and Seymour's 6-flow theorem

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  25. Canonical streaming enumeration of eligible detections

    Idris Ali Shaik

    Palomar RegistryOct 21, 2026cs.DMmachine-checkedscore 0

  26. FixedOrderFactor: the order-r correction factor for mean squares of L(1, chi), and the factor 35/34

    Joseph S. Farland

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  27. Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4 (Theorems 1.1 and 1.2)

    Zijie Zhuang

    Palomar RegistryOct 21, 2026math.PRmachine-checkedscore 0

  28. Wu 2008 Lemma 2.2, Chen's double sieve inequality, with the range of the last sum repaired

    Steve Hubbard

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  29. Lovász's bound on the Shannon capacity

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  30. Formalization of a curved three-dimensional simplex Hilbert transform

    Polona Durcik, Marco Fraccaroli, Joris Roos

    Palomar RegistryOct 21, 2026math.CAmachine-checkedscore 0

  31. Vinogradov's three primes theorem and almost all binary Goldbach, after Heath-Brown 1985, with the Siegel-Walfisz theorem

    Steve Hubbard

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  32. Two-scale Kakeya upper Minkowski lower bound

    Mark Lewko

    Palomar RegistryOct 21, 2026math.CAmachine-checkedscore 0

  33. Lovász's perfect graph theorems

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  34. Improved zero-density estimates for the Riemann zeta function

    Mark Lewko

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  35. The Nash–Williams triangle-decomposition theorem

    Juan Pablo Traverso Gianini

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  36. Chemical heredity without genetic templates

    Michael Mislan

    Palomar RegistryOct 21, 2026math.PRmachine-checkedscore 0

  37. The Riemann hypothesis is equivalent to an asymptotic for the average number of Goldbach representations, after Granville 2007

    Steve Hubbard

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  38. Hermite's signature theorem and the coprime compositum, with the degree-12 compositum of x^3 - x - 1 and x^4 - x - 1

    Stephanie Alexander

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  39. Banach–Mazur determinacy for Baire-property targets

    Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

    Palomar RegistryOct 21, 2026math.GNmachine-checkedscore 0

  40. Bounded conjunction and proper-basis algorithms

    Idris Ali Shaik

    Palomar RegistryOct 21, 2026cs.CCmachine-checkedscore 0

  41. RamanujanNestedRadicals: convergence and exact values of Ramanujan-type nested radicals

    Artur Flamandzki

    Palomar RegistryOct 21, 2026math.CAmachine-checkedscore 0

  42. Ordinary resolution for native encodings and observation wrappers

    Idris Ali Shaik

    Palomar RegistryOct 21, 2026cs.CCmachine-checkedscore 0

  43. Induced Erdős–Sauer: an n log log n bound

    Matija Bucic, Fankang He, Hyunwoo Lee

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  44. Erdős #257: irrationality for every reciprocal-summable support and every integer base

    Will Cook

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  45. Erdős #269: exact three-prime running-LCM identity and infinite kernel rank

    Will Cook

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  46. Erdős problem #257: all base irrationality of the reciprocal Mersenne subseries for every infinite reciprocal summable support, with weighted mass and positive cover extensions, achievement set geometry, and exact greedy membership criteria

    Will Cook

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  47. All-base bases and integral relations for the totient kernel

    Will Cook

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  48. Kriz-Nordentoft non-vanishing for twists of elliptic curve L-series

    David Loeffler

    Palomar RegistryOct 21, 2026math.NTmachine-checkedscore 0

  49. Selected Sidon subset theorems of Ma–Tang (partial paper formalization)

    AItoBit

    Palomar RegistryOct 21, 2026math.COmachine-checkedscore 0

  50. Symplectic Stafford: the affine same-divisor theorem

    Christopher Albert

    Palomar RegistryOct 21, 2026math.RAmachine-checkedscore 0

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