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.   download link      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 2^r-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   x^ry^s  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 ₃ F₂ (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 ₂ F₁ 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    mr3857590

(118)    R. J. Evans and Nolan Wallach,   Pfaffians for Toeplitz payoff matrices,
Linear Algebra and its Applications 577 (2019), 114--120.   pdf    mr3945627

(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    mr4065453

(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    mr4246523

(121)   R. J. Evans, F. Lemmermeyer, Z.-H. Sun, and M. Van Veen,   Ring class fields and a result of Hasse,
J. Number Theory 266 (2025), 33--61.   pdf    mr4788240

(122)   R. J. Evans and M. Van Veen,   Jacobi symbols on class groups of quadratic forms,
Acta Arith. (to appear).   pdf

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