Publications of Richard H. Hudson

(Some reviews are available through MathSciNet)

  1. Bays, Carter; Hudson, Richard H., A new bound for the smallest $x$ with $\pi(x) > \mathrm{li}(x)$. Math. Comp. , posted on May 4, 1999 (to appear in print)

  2. Bays, Carter; Hudson, Richard H., Zeroes of Dirichlet $L$-functions and irregularities in the distribution of primes. Math. Comp. , posted on March 10, 1999 (to appear in print)

  3. Williams, Kenneth S.; Hudson, Richard H., Representation of primes by the principal form of discriminant $-D$ when the class number $h(-D)$ is $3$. Acta Arith. 57 (1991), no. 2, 131--153.

  4. Hudson, R. H.; Williams, K. S., The integers of a cyclic quartic field. Rocky Mountain J. Math. 20 (1990), no. 1, 145--150.

  5. Hardy, Kenneth; Hudson, Richard H.; Richman, David; Williams, Kenneth S., Determination of all imaginary cyclic quartic fields with class number $2$. Trans. Amer. Math. Soc. 311 (1989), no. 1, 1--55.

  6. Hardy, Kenneth; Hudson, R. H.; Richman, D.; Williams, Kenneth S.; Holtz, N. M., Calculation of the class numbers of imaginary cyclic quartic fields. Math. Comp. 49 (1987), no. 180, 615--620.

  7. Hudson, Richard H., Convergence of tribonacci decimal expansions. Fibonacci Quart. 25 (1987), no. 2, 163--170.

  8. Buell, Duncan A.; Hudson, Richard H., Sequences in power residue classes. Internat. J. Math. Math. Sci. 9 (1986), no. 2, 261--266.

  9. Hudson, Richard H., Products and sums of powers of binomial coefficients mod $p$ and solutions of certain quaternary Diophantine systems. Math. Comp. 43 (1984), no. 168, 603--613.

  10. Buell, Duncan A.; Hudson, Richard H., Solutions of certain quaternary quadratic systems. Pacific J. Math. 114 (1984), no. 1, 23--45.

  11. Buell, Duncan A.; Hudson, Richard H., On runs of consecutive quadratic residues and quadratic nonresidues BIT 24 (1984), no. 2, 243--247.

  12. Buell, Duncan A.; Hudson, Richard H.; Williams, Kenneth S., Extension of a theorem of Cauchy and Jacobi. J. Number Theory 19 (1984), no. 3, 309--340.

  13. Hudson, Richard H., Averaging effects on irregularities in the distribution of primes in arithmetic progressions. Math. Comp. 44 (1985), no. 170, 561--571.

  14. Hudson, Richard H.; Williams, Kenneth S., Binomial coefficients and Jacobi sums. Trans. Amer. Math. Soc. 281 (1984), no. 2, 431--505.

  15. Hudson, Richard H.; Markham, Thomas L., Alfred T. Brauer as a mathematician and teacher. Linear Algebra Appl. 59 (1984), 1--17.

  16. Hudson, Richard H., Class numbers of imaginary cyclic quartic fields and related quaternary systems. Pacific J. Math. 115 (1984), no. 1, 129--142.

  17. Hudson, Richard H., On the first occurrence of certain patterns of quadratic residues and nonresidues. Israel J. Math. 44 (1983), no. 1, 23--32.

  18. Hudson, Richard H., Diophantine determinations of $3\sp{(p-1)/8}$ and $5\sp{(p-1)/4}$. Pacific J. Math. 111 (1984), no. 1, 49--55.

  19. Hudson, Richard H., A note on prime $k$th power nonresidues. Manuscripta Math. 42 (1983), no. 2-3, 285--288.

  20. Hudson, Richard H.; Williams, Kenneth S., On Legendre's equation $ax\sp{2}+by\sp{2}+cz\sp{2}=0$. J. Number Theory 16 (1983), no. 1, 100--105.

  21. Hudson, Richard H.; Williams, Kenneth S., Extensions of theorems of Cunningham\mhy Aigner and Hasse\mhy Evans. Pacific J. Math. 104 (1983), no. 1, 111--132.

  22. Bays, Carter; Hudson, Richard H., The cyclic behavior of primes in the arithmetic progressions modulo $11$. J. Reine Angew. Math. 339 (1983), 215--220.

  23. Hudson, Richard H.; Williams, Kenneth S., Class number formulae of Dirichlet type. Math. Comp. 39 (1982), no. 160, 725--732.

  24. Hudson, Richard H., A theorem on totally multiplicative functions. Manuscripta Math. 36 (1981/82), no. 3, 323--346.

  25. Hudson, Richard H.; Williams, Kenneth S., Congruences for representations of primes by binary quadratic forms. Acta Arith. 41 (1982), no. 4, 311--322.

  26. Hudson, R. H.; Williams, K. S., An application of a formula of Western to the evaluation of certain Jacobsthal sums. Acta Arith. 41 (1982), no. 3, 261--276.

  27. Hudson, Richard H.; Williams, Kenneth S., A new formulation of the law of octic reciprocity for primes $\equiv \2613$ $({\rm mod}\,8)$ and its consequences. Internat. J. Math. Math. Sci. 5 (1982), no. 3, 565--584.

  28. Hudson, Richard H.; Williams, Kenneth S., A divisibility property of binomial coefficients viewed as an elementary sieve. Internat. J. Math. Math. Sci. 4 (1981), no. 4, 731--743.

  29. Hudson, Richard H.; Williams, Kenneth S., Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums. Pacific J. Math. 99 (1982), no. 2, 379--386.

  30. Hudson, Richard H.; Williams, Kenneth S., Cauchy-type congruences for binomial coefficients. Proc. Amer. Math. Soc. 85 (1982), no. 2, 169--174.

  31. Hudson, Richard H., On a conjecture of Emma Lehmer. Manuscripta Math. 35 (1981), no. 3, 353--370.

  32. Hudson, Richard H.; Winans, C. F., A complete characterization of the decimal fractions that can be represented as $\sum 10\sp{-k(i+1)}F\sb{\alpha i}$, where $F\sb{\alpha i}$ is the $\alpha i$th Fibonacci number. Fibonacci Quart. 19 (1981), no. 5, 414--421.

  33. Hudson, Richard H., A common combinatorial principle underlies Riemann's formula, the Chebyshev phenomenon, and other subtle effects in comparative prime number theory. I. (French) J. Reine Angew. Math. 313 (1980), 133--150.

  34. Hudson, Richard H.; Williams, Kenneth S., Some new residuacity criteria. Pacific J. Math. 91 (1980), no. 1, 135--143.

  35. Hudson, Richard H.; Williams, Kenneth S., A new criterion for $7$ to be a fourth power (mod $p$). Israel J. Math. 38 (1981), no. 3, 221--230.

  36. Hudson, Richard H.; Williams, Kenneth S., On the least quadratic nonresidue of a prime $p\equiv 3$ $({\rm mod}$ $4)$. J. Reine Angew. Math. 318 (1980), 106--109.

  37. Bays, Carter; Hudson, Richard H., Numerical and graphical description of all axis crossing regions for the moduli $4$ and $8$ which occur before $10\sp{12}$. Internat. J. Math. Math. Sci. 2 (1979), no. 1, 111--119.

  38. Hudson, Richard H., On a conjecture of Issai Schur. J. Reine Angew. Math. 289 (1977), 215--220.

  39. Bays, Carter; Hudson, Richard H., Details of the first region of integers $x$ with $\pi \sb{3,2}(x)<\pi \sb{3,1}(x)$. Math. Comp. 32 (1978), no. 142, 571--576.

  40. Bays, Carter; Hudson, Richard H., On the fluctuations of Littlewood for primes of the form $4n\not=1$. Math. Comp. 32 (1978), no. 141, 281--286.

  41. Bays, Carter; Hudson, Richard H., The appearance of tens of billions of integers $x$ with $\pi \sb{24,13}(x)<\pi \sb{24,1}(x)$ in the vicinity of $10\sp{12}$. J. Reine Angew. Math. 299/300 (1978), 234--237.

  42. Hudson, Richard H.; Bays, Carter, The mean behavior of primes in arithmetic progressions. J. Reine Angew. Math. 296 (1977), 80--99.

  43. Bays, Carter; Hudson, Richard H., The segmented sieve of Eratosthenes and primes in arithmetic progressions to $10\sp{12}$. Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 2, 121--127.

  44. Hudson, Richard H.; Brauer, Alfred, On the exact number of primes in the arithmetic progressions $4n\2611$ and $6n\2611$. J. Reine Angew. Math. 291 (1977), 23--29.

  45. Hudson, Richard H., A formula for the exact number of primes below a given bound in any arithmetic progression. Bull. Austral. Math. Soc. 16 (1977), no. 1, 67--73.

  46. Hudson, Richard H., A sharper bound for the least pair of consecutive $k$-th power non-residues of non-principal characters $({\rm mod}$ $p)$ of order $k>3$. Acta Arith. 30 (1976), no. 2, 133--135.

  47. Hudson, Richard H., Generalizations of a classical theorem in number theory. Math. Comp. 30 (1976), no. 135, 649--656.

  48. Hudson, Richard H., The least pair of consecutive character non-residues. J. Reine Angew. Math. 281 (1976), 219--220.

  49. Hudson, Richard H., A bound for the first $k-1$ consecutive $k$-th power non-residues $({\rm mod}\,p)$. Acta Arith. 28 (1975/76), no. 3, 341--343.

  50. Hudson, Richard H., Power residues and nonresidues in arithmetic progressions. Trans. Amer. Math. Soc. 194 (1974), 277--289.

  51. Hudson, Richard H., A note on the second smallest prime $k$th power nonresidue. Proc. Amer. Math. Soc. 46 (1974), 343--346.

  52. Hudson, Richard H., On the least $k$th power non-residue. Ark. Mat. 12 (1974), 217--220.

  53. Hudson, Richard H., Totally multiplicative sequences with values $\2611$ which exclude four consecutive values of $1$. J. Reine Angew. Math. 271 (1974), 218--220.

  54. Hudson, Richard H., A note on Dirichlet characters. Math. Comp. 27 (1973), 973--975.

  55. Hudson, Richard H., Prime $k$-th power non-residues. Acta Arith. 23 (1973), 89--106.

  56. Hudson, Richard H., On the distribution of $k$-th power non residues in the interval $[1,\,p\sp{a}],\,2/5 < a\leq 4/9$. J. Reine Angew. Math. 260 (1973), 178--180.

  57. Hudson, Richard H., A bound for the first occurrence of three consecutive integers with equal quadratic character. Duke Math. J. 40 (1973), 33--39.

  58. Hudson, Richard H., On the distribution of $k$-th power nonresidues. Duke Math. J. 39 (1972), 85--88.

  59. Hudson, Richard H., On sequences of consecutive quadratic nonresidues. J. Number Theory 3 (1971), 178--181.