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.
pdf
MR47#8408
(3) R. J. Evans, Modular forms on Hecke's modular groups,
Proc. Amer. Math. Soc. 37 (1973), 411-412.
pdf
MR46#8977
(4) R. J. Evans, A fundamental region for Hecke's modular
group,
J. Number Theory 5 (1973), 108-115.
pdf
MR47#3319
(5) R. J. Evans, An asymptotic formula for extended Eulerian
numbers,
Duke Math. J. 41 (1974), 161-175.
pdf
MR48#11014
(6) R. J. Evans, Free products of two real cyclic matrix
groups,
Glasgow Math. J. 15 (1974), 121-128.
pdf
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.
pdf
MR54#332
(13) R. J. Evans, Polynomial sums over automorphs
of a positive definite binary quadratic form,
J. Number Theory 9 (1977), 61-62.
pdf
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.
pdf
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.
pdf
MR57#5905
(17) R. J. Evans, Bender's generalized
q-binomial Vandermonde convolution,
Aeq. Math. 17 (1978), 331-335.
view
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.
pdf
MR80k:12030
(19) R. J. Evans, An asymptotic formula for a sum
of products of powers,
Canadian Math. Bull. 21 (1978), 427-433.
pdf
MR80e:10017
(20) R. J. Evans, Discrete free products
of two complex cyclic matrix groups,
Glasgow Math. J. 20 (1979), 69-80.
pdf
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.
pdf
MR80b:10053
(23) R. J. Evans, Non-free groups generated
by two parabolic matrices,
J. Research Nat. Bur. Standards 84 (1979), 179-180.
pdf
MR80h:20069
(24) R. J. Evans, Resolution of
sign ambiguities in Jacobi and Jacobsthal sums,
Pacific J. Math. 81 (1979), 71-80.
pdf
MR81a:10051
(25) B. C. Berndt and R. J. Evans, Sums of Gauss,
Jacobi and Jacobsthal,
J. Number Theory 11 (1979), 349-398.
pdf
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.
pdf
MR81j:10055
(27) R. J. Evans, Unambiguous evaluations
of bidecic Jacobi and Jacobsthal sums,
J. Australian Math. Soc. (Series A) 28 (1979), 235-240.
pdf
MR81c:10042
(28) R. J. Evans, Bioctic Gauss sums
and sixteenth power residue difference sets,
Acta Arith. 38 (1980), 37-46.
pdf
MR81h:10004
(29) R. J. Evans, The 2r-th
power character of 2,
J. Reine Angew. Math. 315 (1980), 174-189.
view
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.
pdf
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.
pdf
MR83h:10006
(34) R. J. Evans, Generalized cyclotomic periods,
Proc. Amer. Math. Soc. 81 (1981), 207-212.
pdf
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.
pdf
MR83c:05075
(36) B. C. Berndt and R. J. Evans,
The determination of Gauss sums,
Bull. Amer. Math. Soc. 5 (1981), 107-129.
pdf Corrigendum.pdf
MR82h:10051
(37) R. J. Evans, Identities
for products of Gauss sums over finite fields,
Enseignement Math. 27 (1981), 197-209.
view
MR83i:10050
(38) R. J. Evans,
On additive partitions of the positive integers,
Discrete Math. 36 (1981), 239-245.
pdf
MR83m:10014
(39) R. J. Evans, Pure Gauss sums over finite fields,
Mathematika 28 (1981), 239-248.
pdf
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.
pdf
MR83k:33001
(41) R. J. Evans,
Period polynomials for generalized cyclotomic periods,
Manuscripta Math. 40 (1982), 217-243.
pdf
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.
pdf
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.
pdf
MR86d:11020
(44) R. J. Evans,
Twenty-fourth power residue difference sets,
Math. Comp. 40 (1983), 677-683.
pdf
MR84e:12024
(45) R. J. Evans, The octic period polynomial,
Proc. Amer. Math. Soc. 87 (1983), 389-393.
pdf
MR84b:10055
(46) R. J. Evans,
Character sum analogues
of constant term identities for root systems,
Israel J. Math. 46 (1983), 189-196.
pdf
MR85c:11073
(47) R. J. Evans, Determinations of Jacobsthal sums,
Pacific J. Math. 110 (1984), 49-58.
pdf
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.
pdf
MR86d:30015
(49) R. J. Evans and D. Stanton, Asymptotic formulas
for zero-balanced hypergeometric series,
SIAM J. Math Anal. 15 (1984), 1010-1020.
pdf
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.
view
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.
pdf
MR88a:20047
(54) R. J. Evans, Hermite character sums,
Pacific J. Math. 122 (1986), 357-390.
pdf
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.
pdf
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.
pdf
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.
pdf
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.
pdf
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.
pdf
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.
pdf
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.
pdf
MR92d:33043
(68) R. J. Evans, The evaluation of
Selberg character sums,
Enseignement Math. 37 (1991), 235-248.
view
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.
pdf
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.
pdf
MR93a:90082
(71) R. J. Evans and J. J. Wavrik,
Zeros of difference polynomials,
J. Approx. Theory 69 (1992), 1-14.
pdf
MR93d:30006
(72) R. J. Evans, A character sum for root
system G2,
Proc. Amer. Math. Soc. 114 (1992), 627-635.
pdf
MR92f:11114
(73) R. J. Evans, Multidimensional
q-beta integrals,
SIAM J. Math. Anal. 23 (1992), 758-765.
pdf
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.
pdf
MR93j:11080
(75) R. J. Evans, K. Stolarsky and J. Wavrik,
Difference polynomials,
Contemp. Math. 143 (1993), 329-346.
pdf
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.
pdf
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.
pdf
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.
pdf
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.
pdf
MR2001b:05038
(87) R. J. Evans,
Nonexistence of twentieth power residue difference sets,
Acta Arith. 84 (1999), 397-402.
pdf
MR2000j: 11189
(88) R. J. Evans,
Classical congruences for parameters in binary quadratic forms,
Finite Fields and their Applications 7 (2001), 110-124.
pdf
MR2001i: 11043
(89) R. J. Evans, Gauss sums of orders six and twelve,
Canadian Math. Bull. 44 (2001), 22-26.
pdf
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.
pdf
MR2002f: 11105
(91) R. J. Evans,
Extensions of classical congruences for parameters in binary quadratic forms,
Acta Arith. 100 (2001), 349-364.
pdf
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.
pdf
MR2005a: 11172
(94) R. J. Evans, M. Minei, and
B. Yee, Incomplete higher order Gauss sums,
J. Math. Anal. Appl. 281 (2003), 454-476.
pdf
MR2004e: 11086
(95) R. J. Evans and J. Pearlman, Nonexistence of odd perfect
numbers of a certain form,
Fibonacci Quarterly 45 (2007), 122-127.
pdf
2009c: 11008
(96) H. Timothy Choi and R. J. Evans, Congruences for sums of powers of Kloosterman sums,
International Journal of Number Theory 3 (2007), 105-117.
pdf
2008d: 11090
(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.
pdf
2008k: 11040
(98) 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.
pdf
2008m: 22002
(99) R. J. Evans and J. Greene,
Clausen's theorem and hypergeometric functions over finite fields,
Finite Fields Appl. 15 (2009), 97-109.
pdf
mr2468995
(100) R. J. Evans and J. Greene, Evaluations of
hypergeometric functions over finite fields,
Hiroshima Math. J. 39 (2009), 217-235.
pdf
mr2543651 Corrigenda
On the fourth line of the proof of Theorem 2.4,
the misprint $\overline{A}C^2$
should be corrected to $\overline{A}C$.
The penultimate sentence preceding Theorem 1.1 should begin:
"However, because every element of $F_{q}$ is a square in $F_{q^2}$, it is
always possible..." Moreover, in that same sentence, "(3.2)--(3.3)" should
be replaced by "(2.16)--(2.17)".
(101) R. J. Evans and Frank Lam, Special values of
hypergeometric functions over finite fields,
Ramanujan Journal 19 (2009), 151-162.
pdf
mr2511668
(102) R. J. Evans, Seventh power moments of Kloosterman sums,
Israel J. Math. 175 (2010), 349-362.
pdf
mr2607549
(103) R. J. Evans, Hypergeometric 3F2(1/4) evaluations
over finite fields and Hecke eigenforms,
Proc. Amer. Math. Soc. 138 (2010), 517-531.
pdf
mr2557169
(104) K. Byard, R. J. Evans, and M. Van Veen,
Lam's power residue addition sets,
Adv. Appl. Math. 46 (2011), 94-108.
pdf
mr2794016
(105) R. J. Evans, Fourier coefficients of
Hecke eigenforms,
Functiones et Approximatio 46.2 (2012), 147-159.
pdf
mr2931662
(106)
Amanda Bower, R. J. Evans, Victor Luo, and Steven J. Miller,
Coordinate sum and difference sets of d-dimensional modular hyperbolas,
Integers 13 (2013), A31.
pdf
mr3097145
(107) R. J. Evans, Gauss, Jacobi, and Kloosterman sums,
Handbook of Finite Fields, Section 6.1, G. L. Mullen and
D. Panario, eds.,
CRC Press, Boca Raton, FL, 2013.
mr3087321
(108) R. J. Evans, Lihua Huang, and Tuan Nguyen,
Keeler's theorem and products of distinct transpositions,
Amer. Math. Monthly 121 (2014), 136--144.
pdf
mr3149031
(109) R. J. Evans and Lihua Huang,
Mind switches in Futurama and Stargate,
Mathematics Magazine 87 (2014), 252--262.
pdf fig1.pdf
mr3275787
(110) R. J. Evans and K. S. Williams,
Quartic residuacity and the quadratic character of
certain quadratic irrationalities,
Int. J. Number Theory 8 (2015), 2487--2503.
pdf
mr3420756
(111) R. J. Evans and John Greene,
A quadratic hypergeometric 2F1 transformation over finite fields,
Proc. Amer. Math. Soc. 145, No. 3, (2017), 1071--1076.
pdf
mr3589307
(112) R. J. Evans and John Greene,
Some mixed character sum identities of Katz II,
J. Res. Number Theory (2017) 3:8. doi:10.1007/s40993-016-0071-5
pdf
mr3630725
(113) R. J. Evans and M. Van Veen,
Nonexistence of twenty-fourth power residue addition sets,
Finite Fields Appl. 46 (2017), 139--146.
pdf
mr3655752
(114) R. J. Evans,
Some mixed character sum identities of Katz,
J. Number Theory 179 (2017), 17--32.
pdf
mr3657152
(115) J. Eggers, R. J. Evans, and M. Van Veen,
Classification of certain types of maximal matrix subalgebras,
Linear Algebra and its Applications 532 (2017), 397--405.
pdf
mr3688647
(116) R. J. Evans and M. Van Veen,
Bivariate identities related to Chebyshev and
Dickson polynomials over F_q,
Finite Fields Appl. 49 (2018), 143--155.
pdf
mr3724863
(117) R. J. Evans and M. Van Veen,
Irreducible factorization of translates of reversed Dickson
polynomials over finite fields,
Finite Fields Appl. 54 (2018), 151--175.
pdf
(118) R. J. Evans and Nolan Wallach,
Pfaffians for Toeplitz payoff matrices,
Linear Algebra and its Applications 577 (2019), 114--120.
pdf
(119) R. J. Evans, John Greene, and M. Van Veen,
Nullities for a class of skew-symmetric Toeplitz band matrices,
Linear Algebra and its Applications 593 (2020), 276--304.
pdf
(120) R. J. Evans, John Greene, and M. Van Veen,
Nullities for a class of 0-1 symmetric Toeplitz band matrices,
Electronic Journal of Linear Algebra 37 (2021), 177--192.
pdf
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