SELECTED PUBLICATIONS
OF RONALD J. EVANS (with links to MathSciNet
reviews)
(1) R. J. Evans, On blocks of N consecutive integers,
Amer. Math. Monthly 76 (1969), 48-49.
(2) R. J. Evans, On N consecutive integers in
an arithmetic progression
Acta Sci. Math. (Szeged) 33 (1972), 295-296.
MR47#8408
(3) R. J. Evans, Modular forms on Hecke's modular groups,
Proc. Amer. Math. Soc. 37 (1973), 411-412.
MR46#8977
(4) R. J. Evans, A fundamental region for Hecke's modular
group,
J. Number Theory 5 (1973), 108-115.
MR47#3319
(5) R. J. Evans, An asymptotic formula for extended Eulerian
numbers,
Duke Math. J. 41 (1974), 161-175.
MR48#11014
(6) R. J. Evans, Free products of two real cyclic matrix
groups,
Glasgow Math. J. 15 (1974), 121-128.
MR50#13284
(7) R. J. Evans, A winning opening in reverse Hex,
J. Recreational Math. 7 (1974), 189-192.
(8) B. C. Berndt and R. J. Evans, Least positive residues
and the law of quadratic reciprocity,
Delta 4 (1974), 65-69.
MR50#12881
(9) R. J. Evans, A new proof on the free product structure
of Hecke groups,
Publicationes Math. Debrecen 22 (1975), 41-42.
MR51#13069
(10) R. J. Evans, Some variants of Hex,
J. Recreational Math. 8 (1975), 120-122.
(11) R. J. Evans, Reverse Cram with block
sizes not exceeding 13,
Delta 6 (1976), 57-66.
MR56#8026
(12) R. J. Evans and I. M. Isaacs, Generalized Vandermonde
determinants and roots of unity of prime order,
Proc. Amer. Math. Soc. 58 (1976), 51-54.
MR54#332
(13) R. J. Evans, Polynomial sums over automorphs
of a positive definite binary quadratic form,
J. Number Theory 9 (1977), 61-62.
MR55#263
(14) R. J. Evans and I. M. Isaacs, Fields generated
by linear combinations of roots of unity,
Trans. Amer. Math. Soc. 229 (1977), 249-258.
MR55#10434
(15) R. J. Evans, Generalizations of a theorem of Chowla on
Gaussian sums,
Houston J. Math. 3 (1977), 343-349.
MR58#16600
(16) B. C. Berndt and R. J. Evans,
Dedekind sums and class numbers,
Monatshefte Math. 84 (1977), 265-273.
MR57#5905
(17) R. J. Evans, Bender's generalized
q-binomial Vandermonde convolution,
Aeq. Math. 17 (1978), 331-335.
MR58#254
(18) R. J. Evans and I. M. Isaacs, Fields generated
by linear combinations of roots of unity, II,
Math. Scandinavica 43 (1978), 26-34.
MR80k:12030
(19) R. J. Evans, An asymptotic formula for a sum
of products of powers,
Canadian Math. Bull. 21 (1978), 427-433.
MR80e:10017
(20) R. J. Evans, Discrete free products
of two complex cyclic matrix groups,
Glasgow Math. J. 20 (1979), 69-80.
MR80e:20058
(21) R. J. Evans, Silverman's game on intervals,
Amer. Math. Monthly 86 (1979), 277-281.
MR81b:90156
(22) R. J. Evans and J. R. Hill, The cyclotomic
numbers of order sixteen,
Math. Comp. 33 (1979), 827-835.
MR80b:10053
(23) R. J. Evans, Non-free groups generated
by two parabolic matrices,
J. Research Nat. Bur. Standards 84 (1979), 179-180.
MR80h:20069
(24) R. J. Evans, Resolution of
sign ambiguities in Jacobi and Jacobsthal sums,
Pacific J. Math. 81 (1979), 71-80.
MR81a:10051
(25) B. C. Berndt and R. J. Evans, Sums of Gauss,
Jacobi and Jacobsthal,
J. Number Theory 11 (1979), 349-398.
MR81j:10054
(26) B. C. Berndt and R. J. Evans, Sums of Gauss
Eisenstein, Jacobi, Jacobsthal and Brewer,
Illinois J. Math. 23 (1979), 374-437.
MR81j:10055
(27) R. J. Evans, Unambiguous evaluations
of bidecic Jacobi and Jacobsthal sums,
J. Australian Math. Soc. (Series A) 28 (1979), 235-240.
MR81c:10042
(28) R. J. Evans, Bioctic Gauss sums
and sixteenth power residue difference sets,
Acta Arith. 38 (1980), 37-46.
MR81h:10004
(29) R. J. Evans, The 2r-th
power character of 2,
J. Reine Angew. Math. 315 (1980), 174-189.
MR81f:10006
(30) R. J. Evans,
Note on intersections of translates of powers in finite fields,
Hokkaido Math. J. 9 (1980), 135-137.
MR81m:10074
(31) B. C. Berndt and R. J. Evans, Half Gauss sums,
Math. Annalen 249 (1980), 115-125.
MR81i:10049
(32) R. J. Evans, Table of
cyclotomic numbers of order twenty-four,
Math. Comp. 35 (1980), 1036-1038;
UMT file 12 (9.10), 98 pages.
(33) R. J. Evans, Rational reciprocity laws,
Acta Arith. 39 (1981), 281-294.
MR83h:10006
(34) R. J. Evans, Generalized cyclotomic periods,
Proc. Amer. Math. Soc. 81 (1981), 207-212.
MR82f:10050
(35) R. J. Evans, J. Pulham and J. Sheehan,
On the number
of complete subgraphs contained in certain graphs,
J. Combinatorial Theory (Series B) 30 (1981), 364-371.
MR83c:05075
(36) B. C. Berndt and R. J. Evans,
The determination of Gauss sums,
Bull. Amer. Math. Soc. 5 (1981), 107-129.
MR82h:10051
(37) R. J. Evans, Identities
for products of Gauss sums over finite fields,
Enseignement Math. 27 (1981), 197-209.
MR83i:10050
(38) R. J. Evans,
On additive partitions of the positive integers,
Discrete Math. 36 (1981), 239-245.
MR83m:10014
(39) R. J. Evans, Pure Gauss sums over finite fields,
Mathematika 28 (1981), 239-248.
MR83f:10040
(40) R. J. Evans, M. Ismail and D. Stanton,
Coefficients
in expansions of certain rational functions,
Canadian J. Math. 34 (1982), 1011-1024.
MR83k:33001
(41) R. J. Evans,
Period polynomials for generalized cyclotomic periods,
Manuscripta Math. 40 (1982), 217-243.
MR84d:12004
(42) B. C. Berndt, R. J. Evans and B. M. Wilson, Chapter 3
of Ramanujan's second notebook,
Advances in Math. 49 (1983), 123-169.
MR85c:11020
(43) B. C. Berndt and R. J. Evans, Chapter 7
of Ramanujan's second notebook,
Proc. Indian Acad. Sci. 92 (1983), 67-96.
MR86d:11020
(44) R. J. Evans,
Twenty-fourth power residue difference sets,
Math. Comp. 40 (1983), 677-683.
MR84e:12024
(45) R. J. Evans, The octic period polynomial,
Proc. Amer. Math. Soc. 87 (1983), 389-393.
MR84b:10055
(46) R. J. Evans,
Character sum analogues
of constant term identities for root systems,
Israel J. Math. 46 (1983), 189-196.
MR85c:11073
(47) R. J. Evans, Determinations of Jacobsthal sums,
Pacific J. Math. 110 (1984), 49-58.
MR85d:11077
(48) R. J. Evans and K. B. Stolarsky, A family
of polynomials with concyclic zeros. II,
Proc. Amer. Math. Soc. 92 (1984), 393-396.
MR86d:30015
(49) R. J. Evans and D. Stanton, Asymptotic formulas
for zero-balanced hypergeometric series,
SIAM J. Math Anal. 15 (1984), 1010-1020.
MR85i:33003
(50) B. C. Berndt and R. J. Evans, Chapter 13 of
Ramanujan's second notebook: integrals and asymptotic expansions,
Expositiones Math. 2 (1984), 289-347.
MR86j:01032
(51) R. J. Evans, The octic and bioctic character of
certain quadratic units,
Utilitas Math. 25 (1984), 153-157.
MR86j:11109
(52) B. C. Berndt and R. J. Evans, Extensions of
asymptotic expansions from Chapter 15 of Ramanujan's second notebook,
J. Reine Angew. Math. 361 (1985), 118-134.
MR87b:41031
(53) J. L. Brenner, R. J. Evans and D. M. Silberger,
The universality of words
xrys in alternating groups,
Proc. Amer. Math. Soc. 96 (1986), 23-28.
MR88a:20047
(54) R. J. Evans, Hermite character sums,
Pacific J. Math. 122 (1986), 357-390.
MR87e:11140
(55) R. J. Evans, Congruences for minimal
polynomials of Gauss sums,
Bull. Math. Acad. Sinica 14 (1986), 169-185.
MR87k:11090
(56) S. Chowla, B. Dwork and R. J. Evans, On the
mod p2 determination of
[the binomial coefficient]
((p-1)/2 (p-1)/4),
J. Number Theory 24 (1986), 188-196.
MR88a:11130
(57) B. Berndt and R. J. Evans, Chapter 15 of
Ramanujan's second notebook: part 2, modular forms,
Acta Arith. 47 (1986), 123-142.
MR88d:11039
(58) J. L. Brenner and R. J. Evans, Even permutations
as a product of two elements of order five,
J. Combinatorial Theory (Series A) 45 (1987), 196-206.
MR88g:20005
(59) R. J. Evans, Ramanujan's second notebook:
Asymptotic expansions for hypergeometric series and related functions, in Ramanujan Revisited, (G. Andrews et al., editors),
pp. 537-560, Academic Press, 1988.
MR89c:33003
(60) R. J. Evans and W. A. Root, Conjectures for Selberg
character sums,
J. Ramanujan Math. Soc. 3, No. 1, (1988), 111-128.
MR90e:11120
(61) R. J. Evans,
Solution to Problem 87-6,
The entropy of a Poisson distribution,
SIAM Review 30 (1988), 314-315.
(62) R. J. Evans, Residuacity of primes,
Rocky Mountain J. Math. 19 (1989), 1069-1081.
MR90m:11008
(63) B. C. Berndt and R. J. Evans, An integral functional
equation of Ramanujan related to the dilogarithm, in Number Theory, Richard Mollin, ed., pp. 1-5, de Gruyter,
Berlin, 1990.
MR92f:33002
(64) R. J. Evans, Theta function identities,
J. Math. Anal. Appl. 147 (1990), 97-121.
MR91d:11045
(65) J. Autuore and R. J. Evans,
Evaluations of Selberg character
sums, in Analytic Number Theory, B. C. Berndt et al., eds., pp. 13-21,
Birkhäuser, Boston, MA, 1990.
MR92c:11085
(66) B. C. Berndt and R. J. Evans, Some elegant
approximations and asymptotic formulas of Ramanujan,
J. Comp. Appl. Math. 37 (1991), 35-41.
MR93a:41055
(67) R. J. Evans and J. Greene, Polynomials with
nonnegative coefficients whose zeros have modulus one,
SIAM J. Math. Anal. 22 (1991), 1173-1182.
MR92d:33043
(68) R. J. Evans, The evaluation of
Selberg character sums,
Enseignement Math. 37 (1991), 235-248.
MR93c:11062
(69) B. C. Berndt and R. J. Evans, Asymptotic
expansion of a series of Ramanujan, Proc. Edinburgh Math.
Soc. 35 (1992), 189-199.
MR93i:41020
(70) R. J. Evans and G. A. Heuer,
Silverman's game on discrete sets,
Linear Algebra and its Applications 166 (1992), 217-235.
MR93a:90082
(71) R. J. Evans and J. J. Wavrik,
Zeros of difference polynomials,
J. Approx. Theory 69 (1992), 1-14.
MR93d:30006
(72) R. J. Evans, A character sum for root
system G2,
Proc. Amer. Math. Soc. 114 (1992), 627-635.
MR92f:11114
(73) R. J. Evans, Multidimensional
q-beta integrals,
SIAM J. Math. Anal. 23 (1992), 758-765.
MR93e:33004
(74) R. J. Evans, J. Greene and H. Niederreiter,
Linearized polynomials and permutation polynomials of finite fields,
Michigan Math J. 39 (1992), 405-413.
MR93j:11080
(75) R. J. Evans, K. Stolarsky and J. Wavrik,
Difference polynomials,
Contemp. Math. 143 (1993), 329-346.
MR94a:11029
(76) R. J. Evans, Character sums over finite fields,
in
Finite Fields, Coding Theory, and Advances in Communications
and Computing, G. Mullen and P. Shiue, eds., pp. 57-73,
Marcel Dekker, N.Y., 1993.
MR94c:11118
(77) B. C. Berndt and R. J. Evans,
On Rademacher's multiplier
system for the classical theta function,
Contemp. Math. 166 (1994), 1-7.
MR96b:11060
(78) R. J. Evans, Multidimensional beta and gamma integrals,
Contemp. Math. 166 (1994), 341-357.
MR96e:33036
(79) R. J. Evans,
Character sums as orthogonal eigenfunctions of
adjacency operators for Cayley graphs,
Contemp. Math. 168 (1994), 33-50.
MR95g:11121
(80) R. J. Evans,
Selberg-Jack character sums of dimension 2,
J. Number Theory 54 (1995), 1-11.
MR96m:11068
(81) R. J. Evans, Spherical functions for
finite upper half planes with characteristic 2,
Finite fields and their Applications 1 (1995), 376-394.
MR97i:11119
(82) R. J. Evans, Generalized Lambert series,
Analytic Number Theory, Volume 1
(B. Berndt, H. Diamond, A. Hildebrand, eds.)
pp. 357-370, Birkhäuser, Boston, MA, 1996.
MR97e:33014
(83) J. Angel and R. J. Evans,
Diameters of finite upper half plane graphs,
J. Graph Theory 23 (1996), 129-137.
MR97m:05085
(84) R. J. Evans, Congruences for Jacobi sums,
J. Number Theory 71 (1998), 109-120.
MR99e:11109
(85) B. C. Berndt, R. J. Evans and K. S. Williams,
Gauss and Jacobi Sums, Wiley-Interscience, N. Y., 1998.
MR99d:11092
(86) R. J. Evans, H. Hollmann, C. Krattenthaler, and
Q. Xiang, Gauss sums,
Jacobi sums, and p-ranks of cyclic difference sets,
J. Combinatorial Theory (Series A) 87 (1999), 74-119.
MR2001b:05038
(87) R. J. Evans,
Nonexistence of twentieth power residue difference sets,
Acta Arith. 84 (1999), 397-402.
MR2000j: 11189
(88) R. J. Evans,
Classical congruences for parameters in binary quadratic forms,
Finite Fields and their Applications 7 (2001), 110-124.
MR2001i: 11043
(89) R. J. Evans, Gauss sums of orders six and twelve,
Canadian Math. Bull. 44 (2001), 22-26.
MR2002c: 11095
(90) R. J. Evans,
Gauss sums and Kloosterman sums over residue rings of algebraic integers,
Trans. Amer. Math. Soc. 353 (2001), 4429-4445.
MR2002f: 11105
(91) R. J. Evans,
Extensions of classical congruences for parameters in binary quadratic forms,
Acta Arith. 100 (2001), 349-364.
MR2002j: 11033
(92) R. J. Evans,
Twisted hyper-Kloosterman sums over finite rings of integers,
Number Theory for the Millennium, Proc. Millennial Conf. Number Theory
(Urbana, IL, May 21-26, 2000), Vol. I, pp. 429-448,
M. A. Bennett et al. eds., A. K. Peters, Natick, MA, 2002.
MR2003m: 11125
(93) R. J. Evans, P. Kaplan, and
K. S. Williams, Congruences for quadratic units of norm -1,
Ramanujan Journal 7(3) (2003), 449-453.
MR2005a: 11172
(94) R. J. Evans, M. Minei, and
B. Yee, Incomplete higher order Gauss sums,
J. Math. Anal. Appl. 281 (2003), 454-476.
MR2004e: 11086
(95) H. Timothy Choi and R. J. Evans, Congruences for sums of powers of Kloosterman sums,
International Journal of Number Theory 3 (2007), 105-117.
2008d: 11090
(96) R. J. Evans and Nolan Wallach, Pfaffians and strategies for integer choice games,
Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory,
Edited by Li, Tan, Wallach, Zhu, Lecture Notes Series, Institute for Mathematical Sciences,
National University of Singapore, World Scientific, 2007, pp. 53-72.
(97) R. J. Evans and M. Van Veen, Rational representations of primes by binary quadratic forms,
International Journal of Number Theory 3 (2007), 513-528.
(98) R. J. Evans and J. Pearlman, Nonexistence of odd perfect numbers of a certain form,
Fibonacci Quarterly 45 (2007), 122-127.
(99) R. J. Evans and Frank Lam, Special values of hypergeometric functions over finite fields,
Ramanujan Journal (to appear). pdf
(100) R. J. Evans, Seventh power moments of Kloosterman sums, Israel J. Math. (to appear).
pdf
(101) R. J. Evans and J. Greene, Clausen's theorem and hypergeometric functions over finite fields,
Finite Fields Appl. (to appear). pdf
