×
Compute Distance To:
Author ID: banks.william-d Recent zbMATH articles by "Banks, William D."
Published as: Banks, William D.; Banks, William; Banks, W. D.; Banks, Wiliam D.
Homepage: http://faculty.missouri.edu/~bankswd/
External Links: MGP · ResearchGate · dblp
Documents Indexed: 123 Publications since 1995
Co-Authors: 50 Co-Authors with 109 Joint Publications
1,290 Co-Co-Authors
all top 5

Serials

8 Acta Arithmetica
8 Journal of Number Theory
6 Integers
5 The Quarterly Journal of Mathematics
4 Monatshefte für Mathematik
4 The Ramanujan Journal
3 Colloquium Mathematicum
3 Proceedings of the American Mathematical Society
3 Indagationes Mathematicae. New Series
3 Mathematical Research Letters
3 Journal of the Australian Mathematical Society
3 International Journal of Number Theory
2 Bulletin of the Australian Mathematical Society
2 Canadian Journal of Mathematics
2 Canadian Mathematical Bulletin
2 Compositio Mathematica
2 Glasgow Mathematical Journal
2 Illinois Journal of Mathematics
2 Manuscripta Mathematica
2 Michigan Mathematical Journal
2 Transactions of the American Mathematical Society
2 Forum Mathematicum
2 Experimental Mathematics
2 Turkish Journal of Mathematics
2 Uniform Distribution Theory
1 Houston Journal of Mathematics
1 Israel Journal of Mathematics
1 Journal d’Analyse Mathématique
1 Journal of Mathematical Analysis and Applications
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Periodica Mathematica Hungarica
1 Rocky Mountain Journal of Mathematics
1 Mathematics of Computation
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 Acta Scientiarum Mathematicarum
1 Annales des Sciences Mathématiques du Québec
1 Archiv der Mathematik
1 Archivum Mathematicum
1 The Australian Mathematical Society Gazette
1 Bulletin of the London Mathematical Society
1 Commentarii Mathematici Helvetici
1 Duke Mathematical Journal
1 Functiones et Approximatio. Commentarii Mathematici
1 Journal für die Reine und Angewandte Mathematik
1 Pacific Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Proceedings of the London Mathematical Society. Third Series
1 Hardy-Ramanujan Journal
1 SIAM Journal on Discrete Mathematics
1 IMRN. International Mathematics Research Notices
1 Linear Algebra and its Applications
1 Bulletin of the Polish Academy of Sciences, Mathematics
1 Journal de Théorie des Nombres de Bordeaux
1 Revista Matemática Complutense
1 Journal of Integer Sequences
1 Acta Mathematica Sinica. English Series
1 Pure and Applied Mathematics Quarterly
1 Albanian Journal of Mathematics

Publications by Year

Citations contained in zbMATH Open

93 Publications have been cited 494 times in 355 Documents Cited by Year
Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. Zbl 1250.11064
Banks, William D.; Shparlinski, Igor E.
23
2009
Twisted symmetric-square \(L\)-functions and the nonexistence of Siegel zeros on \(\mathrm{GL}(3)\). Zbl 0880.11045
Banks, William D.
21
1997
Prime numbers with Beatty sequences. Zbl 1167.11010
Banks, William D.; Shparlinski, Igor E.
19
2009
Character sums over integers with restricted \(g\)-ary digits. Zbl 1026.11068
Banks, William D.; Conflitti, Alessandro; Shparlinski, Igor E.
18
2002
Piatetski-Shapiro sequences. Zbl 1327.11062
Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J.
16
2013
A corollary to Bernstein’s theorem and Whittaker functionals on the metaplectic group. Zbl 0944.22007
Banks, William D.
15
1998
Arithmetic properties of numbers with restricted digits. Zbl 1049.11003
Banks, William D.; Shparlinski, Igor E.
15
2004
Block-compatible metaplectic cocycles. Zbl 0914.20039
Banks, William D.; Levy, Jason; Sepanski, Mark R.
15
1999
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
15
2008
Arithmetic functions on Beatty sequences. Zbl 1227.11045
Abercrombie, Alex G.; Banks, William D.; Shparlinski, Igor E.
13
2009
Consecutive primes in tuples. Zbl 1323.11071
Banks, William D.; Freiberg, Tristan; Turnage-Butterbaugh, Caroline L.
13
2015
Exponential sums over Mersenne numbers. Zbl 1060.11045
Banks, William D.; Conflitti, Alessandro; Friedlander, John B.; Shparlinski, Igor E.
12
2004
On group structures realized by elliptic curves over arbitrary finite fields. Zbl 1257.11060
Banks, William D.; Pappalardi, Francesco; Shparlinski, Igor E.
11
2012
On limit points of the sequence of normalized prime gaps. Zbl 1410.11114
Banks, William D.; Freiberg, Tristan; Maynard, James
10
2016
On values taken by the largest prime factor of shifted primes. Zbl 1139.11038
Banks, William D.; Shparlinski, Igor E.
10
2007
Short character sums with Beatty sequences. Zbl 1220.11097
Banks, William D.; Shparlinski, Igor E.
10
2006
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
9
2005
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
9
2010
Non-residues and primitive roots in Beatty sequences. Zbl 1144.11064
Banks, William D.; Shparlinski, Igor E.
9
2006
Almost all palindromes are composite. Zbl 1101.11039
Banks, William D.; Hart, Derrick N.; Sakata, Mayumi
8
2004
Double character sums over elliptic curves and finite fields. Zbl 1171.11046
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
8
2006
Prime divisors in Beatty sequences. Zbl 1198.11083
Banks, William D.; Shparlinski, Igor E.
8
2007
Nonlinear complexity of the Naor-Reingold pseudo-random function. Zbl 1032.94507
Banks, William D.; Griffin, Frances; Lieman, Daniel; Shparlinski, Igor E.
7
1999
Every natural number is the sum of forty-nine palindromes. Zbl 1387.11008
Banks, William D.
7
2016
Character sums with Piatetski-Shapiro sequences. Zbl 1317.11082
Baker, Roger C.; Banks, William D.
7
2015
Heredity of Whittaker models on the metaplectic group. Zbl 0980.22021
Banks, William D.
6
1998
Values of the Euler function in various sequences. Zbl 1197.11125
Banks, William D.; Ford, Kevin; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
6
2005
On the value set of \(n!\) modulo a prime. Zbl 1161.11386
Banks, William D.; Luca, Florian; Shparlinski, Igor E.; Stichtenoth, Henning
6
2005
Exponential and character sums with Mersenne numbers. Zbl 1320.11073
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
6
2012
Composite integers \(n\) for which \(\varphi (n)\mid n-1\). Zbl 1215.11094
Banks, William D.; Luca, Florian
6
2007
Optimal primitive sets with restricted primes. Zbl 1285.11021
Banks, William D.; Martin, Greg
6
2013
Representations of integers as sums of primes from a Beatty sequence. Zbl 1130.11056
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley
6
2007
Piatetski-Shapiro primes from almost primes. Zbl 1342.11078
Baker, Roger C.; Banks, William D.; Guo, Zhenyu V.; Yeager, Aaron M.
6
2014
Prime divisors of palindromes. Zbl 1119.11010
Banks, William D.; Shparlinski, Igor E.
6
2005
Integers without divisors from a fixed arithmetic progression. Zbl 1257.11002
Banks, William D.; Friedlander, John B.; Luca, Florian
5
2008
Almost primes of the form \(\lfloor p^c \rfloor\). Zbl 1355.11099
Banks, William D.; Guo, Victor Z.; Shparlinski, Igor E.
5
2016
Concatenations with binary recurrent sequences. Zbl 1068.11007
Banks, William D.; Luca, Florian
5
2005
Irrationality of power series for various number theoretic functions. Zbl 1072.11002
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
5
2005
Uniform distribution of fractional parts related to pseudoprimes. Zbl 1255.11040
Banks, William D.; Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
5
2009
Coincidences in the values of the Euler and Carmichael functions. Zbl 1195.11128
Banks, William D.; Friedlander, John B.; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
5
2006
Multiplicative structure of values of the Euler function. Zbl 1099.11055
Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
4
2004
Whittaker-Fourier coefficients of metaplectic Eisenstein series. Zbl 1023.11024
Banks, William; Bump, Daniel; Lieman, Daniel
4
2003
Power totients with almost primes. Zbl 1268.11141
Banks, William D.; Luca, Florian
4
2011
The Nicolas and Robin inequalities with sums of two squares. Zbl 1275.11130
Banks, William D.; Hart, Derrick N.; Moree, Pieter; Nevans, C. Wesley
4
2009
Distributional properties of the largest prime factor. Zbl 1090.11059
Banks, William D.; Harman, Glyn; Shparlinski, Igor E.
4
2005
Bounds on short character sums and \(L\)-functions with characters to a powerful modulus. Zbl 1460.11110
Banks, William D.; Shparlinski, Igor E.
3
2019
Congruences and exponential sums with the Euler function. Zbl 1110.11032
Banks, William D.; Shparlinski, Igor E.
3
2004
A variant of NTRU with non-invertible polynomials. Zbl 1033.94510
Banks, William D.; Shparlinski, Igor E.
3
2002
A remark on Giuga’s conjecture and Lehmer’s totient problem. Zbl 1219.11003
Banks, William D.; Nevans, C. Wesley; Pomerance, Carl
3
2009
Carmichael numbers with a square totient. Zbl 1194.11094
Banks, W. D.
3
2009
Average value of the Euler function on binary palindromes. Zbl 1106.11004
Banks, William D.; Shparlinski, Igor E.
3
2006
Congruences and rational exponential sums with the Euler function. Zbl 1193.11095
Banks, William D.; Shparlinski, Igor E.
3
2006
Arithmetic properties of \(\varphi(n)/\lambda(n)\) and the structure of the multiplicative group modulo \(n\). Zbl 1142.11067
Banks, Wiliam D.; Luca, Florian; Shparlinski, Igor E.
3
2006
Character sums with exponential functions over smooth numbers. Zbl 1184.11025
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
3
2006
Congruences with intervals and arbitrary sets. Zbl 1483.11260
Banks, William; Shparlinski, Igor
2
2020
On integers with a special divisibility property. Zbl 1164.11050
Banks, William D.; Luca, Florian
2
2006
Multiplicative character sums with twice-differentiable functions. Zbl 1229.11110
Banks, William D.; Shparlinski, Igor E.
2
2009
An extremely small and efficient identification scheme. Zbl 0963.94511
Banks, William D.; Lieman, Daniel; Shparlinski, Igor E.
2
2000
New examples of noncommutative \(\Lambda(p)\) sets. Zbl 1035.43004
Banks, William D.; Harcharras, Asma
2
2003
Values of arithmetical functions equal to a sum of two squares. Zbl 1076.11053
Banks, William D.; Luca, Florian; Saidak, Filip; Shparlinski, Igor E.
2
2005
Average normalisations of elliptic curves. Zbl 1027.11040
Banks, William D.; Shparlinski, Igor E.
2
2002
Carmichael numbers composed of primes from a Beatty sequence. Zbl 1276.11151
Banks, William D.; Yeager, Aaron M.
2
2011
Carmichael numbers with a totient of the form \(a^2+nb^2\). Zbl 1321.11100
Banks, William D.
2
2012
Uniform distribution of the fractional part of the average prime divisor. Zbl 1088.11062
Banks, William D.; Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2
2005
Sums with convolutions of Dirichlet characters. Zbl 1221.11172
Banks, William D.; Shparlinski, Igor E.
2
2010
Character sums with Beatty sequences on Burgess-type intervals. Zbl 1244.11074
Banks, William D.; Shparlinski, Igor E.
2
2009
Fractional parts of Dedekind sums. Zbl 1419.11072
Banks, William D.; Shparlinski, Igor E.
2
2016
On the congruence \(N \equiv A \pmod{\varphi (N)}\). Zbl 1232.11095
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley
2
2008
Sierpiński and Carmichael numbers. Zbl 1325.11010
Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon
2
2015
Waring’s problem for Beatty sequences and a local to global principle. Zbl 1303.11110
Banks, William D.; Güloğlu, Ahmet M.; Vaughan, Robert C.
2
2014
The Casselman-Shalika formula for a distinguished model. Zbl 0823.22014
Banks, William D.
1
1995
Counting integers with a smooth totient. Zbl 1475.11177
Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E.
1
2019
Consecutive primes and Beatty sequences. Zbl 1444.11190
Banks, William D.; Guo, Victor Z.
1
2018
Smooth values of shifted primes in arithmetic progressions. Zbl 1068.11061
Banks, William D.; Harcharras, Asma; Shparlinski, Igor E.
1
2004
Nonaliquots and Robbins numbers. Zbl 1089.11007
Banks, William D.; Luca, Florian
1
2005
On the norm of an idempotent Schur multiplier on the Schatten class. Zbl 1061.47010
Banks, William D.; Harcharras, Asma
1
2004
On repeated values of the Riemann zeta function on the critical line. Zbl 1318.11110
Banks, William D.; Kang, Sarah
1
2012
Descartes numbers. Zbl 1186.11004
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley; Saidak, Filip
1
2008
Integers with a large smooth divisor. Zbl 1234.11128
Banks, William D.; Shparlinski, Igor E.
1
2007
Values of the Euler function free of \(k\)th powers. Zbl 1193.11090
Banks, William D.; Pappalardi, Francesco
1
2006
Estimates for Wieferich numbers. Zbl 1138.11002
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
1
2007
Exponential sums with polynomial values of the discrete logarithm. Zbl 1162.11039
Banks, William D.; Shparlinksi, Igor E.
1
2007
Sums of prime divisors and Mersenne numbers. Zbl 1194.11097
Banks, William D.; Luca, Florian
1
2007
Zeta functions and asymptotic additive bases with some unusual sets of primes. Zbl 1423.11146
Banks, William D.
1
2018
Convolutions with probability distributions, zeros of \(L\)-functions, and the least quadratic nonresidue. Zbl 1406.11082
Banks, William D.; Makarov, Konstantin A.
1
2016
Quadratic nonresidues below the Burgess bound. Zbl 1416.11011
Banks, William D.; Guo, Victor Z.
1
2017
Roughly squarefree values of the Euler and Carmichael functions. Zbl 1163.11339
Banks, William D.; Luca, Florian
1
2005
Some divisibility properties of the Euler function. Zbl 1122.11061
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
1
2005
Sums and products with smooth numbers. Zbl 1273.11044
Banks, William D.; Covert, David J.
1
2011
Distribution of inverses in polynomial rings. Zbl 1095.13534
Banks, William D.; Shparlinski, Igor E.
1
2001
On the number of sparse RSA exponents. Zbl 1033.11045
Banks, William D.; Shparlinski, Igor E.
1
2002
Carmichael meets Chebotarev. Zbl 1370.11108
Banks, William D.; Güloğlu, Ahmet M.; Yeager, Aaron M.
1
2013
Symmetric primes revisited. Zbl 1462.11070
Banks, William; Pollack, Paul; Pomerance, Carl
1
2019
Congruences with intervals and arbitrary sets. Zbl 1483.11260
Banks, William; Shparlinski, Igor
2
2020
Bounds on short character sums and \(L\)-functions with characters to a powerful modulus. Zbl 1460.11110
Banks, William D.; Shparlinski, Igor E.
3
2019
Counting integers with a smooth totient. Zbl 1475.11177
Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E.
1
2019
Symmetric primes revisited. Zbl 1462.11070
Banks, William; Pollack, Paul; Pomerance, Carl
1
2019
Consecutive primes and Beatty sequences. Zbl 1444.11190
Banks, William D.; Guo, Victor Z.
1
2018
Zeta functions and asymptotic additive bases with some unusual sets of primes. Zbl 1423.11146
Banks, William D.
1
2018
Quadratic nonresidues below the Burgess bound. Zbl 1416.11011
Banks, William D.; Guo, Victor Z.
1
2017
On limit points of the sequence of normalized prime gaps. Zbl 1410.11114
Banks, William D.; Freiberg, Tristan; Maynard, James
10
2016
Every natural number is the sum of forty-nine palindromes. Zbl 1387.11008
Banks, William D.
7
2016
Almost primes of the form \(\lfloor p^c \rfloor\). Zbl 1355.11099
Banks, William D.; Guo, Victor Z.; Shparlinski, Igor E.
5
2016
Fractional parts of Dedekind sums. Zbl 1419.11072
Banks, William D.; Shparlinski, Igor E.
2
2016
Convolutions with probability distributions, zeros of \(L\)-functions, and the least quadratic nonresidue. Zbl 1406.11082
Banks, William D.; Makarov, Konstantin A.
1
2016
Consecutive primes in tuples. Zbl 1323.11071
Banks, William D.; Freiberg, Tristan; Turnage-Butterbaugh, Caroline L.
13
2015
Character sums with Piatetski-Shapiro sequences. Zbl 1317.11082
Baker, Roger C.; Banks, William D.
7
2015
Sierpiński and Carmichael numbers. Zbl 1325.11010
Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon
2
2015
Piatetski-Shapiro primes from almost primes. Zbl 1342.11078
Baker, Roger C.; Banks, William D.; Guo, Zhenyu V.; Yeager, Aaron M.
6
2014
Waring’s problem for Beatty sequences and a local to global principle. Zbl 1303.11110
Banks, William D.; Güloğlu, Ahmet M.; Vaughan, Robert C.
2
2014
Piatetski-Shapiro sequences. Zbl 1327.11062
Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J.
16
2013
Optimal primitive sets with restricted primes. Zbl 1285.11021
Banks, William D.; Martin, Greg
6
2013
Carmichael meets Chebotarev. Zbl 1370.11108
Banks, William D.; Güloğlu, Ahmet M.; Yeager, Aaron M.
1
2013
On group structures realized by elliptic curves over arbitrary finite fields. Zbl 1257.11060
Banks, William D.; Pappalardi, Francesco; Shparlinski, Igor E.
11
2012
Exponential and character sums with Mersenne numbers. Zbl 1320.11073
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
6
2012
Carmichael numbers with a totient of the form \(a^2+nb^2\). Zbl 1321.11100
Banks, William D.
2
2012
On repeated values of the Riemann zeta function on the critical line. Zbl 1318.11110
Banks, William D.; Kang, Sarah
1
2012
Power totients with almost primes. Zbl 1268.11141
Banks, William D.; Luca, Florian
4
2011
Carmichael numbers composed of primes from a Beatty sequence. Zbl 1276.11151
Banks, William D.; Yeager, Aaron M.
2
2011
Sums and products with smooth numbers. Zbl 1273.11044
Banks, William D.; Covert, David J.
1
2011
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
9
2010
Sums with convolutions of Dirichlet characters. Zbl 1221.11172
Banks, William D.; Shparlinski, Igor E.
2
2010
Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height. Zbl 1250.11064
Banks, William D.; Shparlinski, Igor E.
23
2009
Prime numbers with Beatty sequences. Zbl 1167.11010
Banks, William D.; Shparlinski, Igor E.
19
2009
Arithmetic functions on Beatty sequences. Zbl 1227.11045
Abercrombie, Alex G.; Banks, William D.; Shparlinski, Igor E.
13
2009
Uniform distribution of fractional parts related to pseudoprimes. Zbl 1255.11040
Banks, William D.; Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
5
2009
The Nicolas and Robin inequalities with sums of two squares. Zbl 1275.11130
Banks, William D.; Hart, Derrick N.; Moree, Pieter; Nevans, C. Wesley
4
2009
A remark on Giuga’s conjecture and Lehmer’s totient problem. Zbl 1219.11003
Banks, William D.; Nevans, C. Wesley; Pomerance, Carl
3
2009
Carmichael numbers with a square totient. Zbl 1194.11094
Banks, W. D.
3
2009
Multiplicative character sums with twice-differentiable functions. Zbl 1229.11110
Banks, William D.; Shparlinski, Igor E.
2
2009
Character sums with Beatty sequences on Burgess-type intervals. Zbl 1244.11074
Banks, William D.; Shparlinski, Igor E.
2
2009
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
15
2008
Integers without divisors from a fixed arithmetic progression. Zbl 1257.11002
Banks, William D.; Friedlander, John B.; Luca, Florian
5
2008
On the congruence \(N \equiv A \pmod{\varphi (N)}\). Zbl 1232.11095
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley
2
2008
Descartes numbers. Zbl 1186.11004
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley; Saidak, Filip
1
2008
On values taken by the largest prime factor of shifted primes. Zbl 1139.11038
Banks, William D.; Shparlinski, Igor E.
10
2007
Prime divisors in Beatty sequences. Zbl 1198.11083
Banks, William D.; Shparlinski, Igor E.
8
2007
Composite integers \(n\) for which \(\varphi (n)\mid n-1\). Zbl 1215.11094
Banks, William D.; Luca, Florian
6
2007
Representations of integers as sums of primes from a Beatty sequence. Zbl 1130.11056
Banks, William D.; Güloğlu, Ahmet M.; Nevans, C. Wesley
6
2007
Integers with a large smooth divisor. Zbl 1234.11128
Banks, William D.; Shparlinski, Igor E.
1
2007
Estimates for Wieferich numbers. Zbl 1138.11002
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
1
2007
Exponential sums with polynomial values of the discrete logarithm. Zbl 1162.11039
Banks, William D.; Shparlinksi, Igor E.
1
2007
Sums of prime divisors and Mersenne numbers. Zbl 1194.11097
Banks, William D.; Luca, Florian
1
2007
Short character sums with Beatty sequences. Zbl 1220.11097
Banks, William D.; Shparlinski, Igor E.
10
2006
Non-residues and primitive roots in Beatty sequences. Zbl 1144.11064
Banks, William D.; Shparlinski, Igor E.
9
2006
Double character sums over elliptic curves and finite fields. Zbl 1171.11046
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
8
2006
Coincidences in the values of the Euler and Carmichael functions. Zbl 1195.11128
Banks, William D.; Friedlander, John B.; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
5
2006
Average value of the Euler function on binary palindromes. Zbl 1106.11004
Banks, William D.; Shparlinski, Igor E.
3
2006
Congruences and rational exponential sums with the Euler function. Zbl 1193.11095
Banks, William D.; Shparlinski, Igor E.
3
2006
Arithmetic properties of \(\varphi(n)/\lambda(n)\) and the structure of the multiplicative group modulo \(n\). Zbl 1142.11067
Banks, Wiliam D.; Luca, Florian; Shparlinski, Igor E.
3
2006
Character sums with exponential functions over smooth numbers. Zbl 1184.11025
Banks, William D.; Friedlander, John B.; Garaev, Moubariz Z.; Shparlinski, Igor E.
3
2006
On integers with a special divisibility property. Zbl 1164.11050
Banks, William D.; Luca, Florian
2
2006
Values of the Euler function free of \(k\)th powers. Zbl 1193.11090
Banks, William D.; Pappalardi, Francesco
1
2006
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
9
2005
Values of the Euler function in various sequences. Zbl 1197.11125
Banks, William D.; Ford, Kevin; Luca, Florian; Pappalardi, Francesco; Shparlinski, Igor E.
6
2005
On the value set of \(n!\) modulo a prime. Zbl 1161.11386
Banks, William D.; Luca, Florian; Shparlinski, Igor E.; Stichtenoth, Henning
6
2005
Prime divisors of palindromes. Zbl 1119.11010
Banks, William D.; Shparlinski, Igor E.
6
2005
Concatenations with binary recurrent sequences. Zbl 1068.11007
Banks, William D.; Luca, Florian
5
2005
Irrationality of power series for various number theoretic functions. Zbl 1072.11002
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
5
2005
Distributional properties of the largest prime factor. Zbl 1090.11059
Banks, William D.; Harman, Glyn; Shparlinski, Igor E.
4
2005
Values of arithmetical functions equal to a sum of two squares. Zbl 1076.11053
Banks, William D.; Luca, Florian; Saidak, Filip; Shparlinski, Igor E.
2
2005
Uniform distribution of the fractional part of the average prime divisor. Zbl 1088.11062
Banks, William D.; Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E.
2
2005
Nonaliquots and Robbins numbers. Zbl 1089.11007
Banks, William D.; Luca, Florian
1
2005
Roughly squarefree values of the Euler and Carmichael functions. Zbl 1163.11339
Banks, William D.; Luca, Florian
1
2005
Some divisibility properties of the Euler function. Zbl 1122.11061
Banks, William D.; Luca, Florian; Shparlinski, Igor E.
1
2005
Arithmetic properties of numbers with restricted digits. Zbl 1049.11003
Banks, William D.; Shparlinski, Igor E.
15
2004
Exponential sums over Mersenne numbers. Zbl 1060.11045
Banks, William D.; Conflitti, Alessandro; Friedlander, John B.; Shparlinski, Igor E.
12
2004
Almost all palindromes are composite. Zbl 1101.11039
Banks, William D.; Hart, Derrick N.; Sakata, Mayumi
8
2004
Multiplicative structure of values of the Euler function. Zbl 1099.11055
Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
4
2004
Congruences and exponential sums with the Euler function. Zbl 1110.11032
Banks, William D.; Shparlinski, Igor E.
3
2004
Smooth values of shifted primes in arithmetic progressions. Zbl 1068.11061
Banks, William D.; Harcharras, Asma; Shparlinski, Igor E.
1
2004
On the norm of an idempotent Schur multiplier on the Schatten class. Zbl 1061.47010
Banks, William D.; Harcharras, Asma
1
2004
Whittaker-Fourier coefficients of metaplectic Eisenstein series. Zbl 1023.11024
Banks, William; Bump, Daniel; Lieman, Daniel
4
2003
New examples of noncommutative \(\Lambda(p)\) sets. Zbl 1035.43004
Banks, William D.; Harcharras, Asma
2
2003
Character sums over integers with restricted \(g\)-ary digits. Zbl 1026.11068
Banks, William D.; Conflitti, Alessandro; Shparlinski, Igor E.
18
2002
A variant of NTRU with non-invertible polynomials. Zbl 1033.94510
Banks, William D.; Shparlinski, Igor E.
3
2002
Average normalisations of elliptic curves. Zbl 1027.11040
Banks, William D.; Shparlinski, Igor E.
2
2002
On the number of sparse RSA exponents. Zbl 1033.11045
Banks, William D.; Shparlinski, Igor E.
1
2002
Distribution of inverses in polynomial rings. Zbl 1095.13534
Banks, William D.; Shparlinski, Igor E.
1
2001
An extremely small and efficient identification scheme. Zbl 0963.94511
Banks, William D.; Lieman, Daniel; Shparlinski, Igor E.
2
2000
Block-compatible metaplectic cocycles. Zbl 0914.20039
Banks, William D.; Levy, Jason; Sepanski, Mark R.
15
1999
Nonlinear complexity of the Naor-Reingold pseudo-random function. Zbl 1032.94507
Banks, William D.; Griffin, Frances; Lieman, Daniel; Shparlinski, Igor E.
7
1999
A corollary to Bernstein’s theorem and Whittaker functionals on the metaplectic group. Zbl 0944.22007
Banks, William D.
15
1998
Heredity of Whittaker models on the metaplectic group. Zbl 0980.22021
Banks, William D.
6
1998
Twisted symmetric-square \(L\)-functions and the nonexistence of Siegel zeros on \(\mathrm{GL}(3)\). Zbl 0880.11045
Banks, William D.
21
1997
The Casselman-Shalika formula for a distinguished model. Zbl 0823.22014
Banks, William D.
1
1995
all top 5

Cited by 382 Authors

59 Shparlinski, Igor E.
24 Luca, Florian
21 Banks, William D.
12 Pollack, Paul
11 Pomerance, Carl Bernard
7 Baier, Stephan
7 Kaplan, Eyal
7 Lu, Guangshi
6 Friedberg, Solomon
5 Freiberg, Tristan
5 Garaev, Moubariz Z.
5 Jiang, Yujiao
5 Mkaouar, Mohamed
5 Munsch, Marc
5 Pan, Hao
4 Chen, Yonggao
4 Cojocaru, Alina Carmen
4 Dartyge, Cécile
4 Goryashin, Dmitriĭ Viktorovich
4 Guo, Victor Zhenyu
4 Mauduit, Christian
3 Akbal, Yıldırım
3 Aloui, Karam
3 Bell, Jason P.
3 Coons, Michael
3 David, Chantal
3 Friedlander, John Benjamin
3 Ginzburg, David
3 Grau, José María
3 Kerr, Bryce
3 Lichtman, Jared Duker
3 Maynard, James
3 Ostafe, Alina
3 Pintz, Janos
3 Pongsriiam, Prapanpong
3 Sárközy, András
3 Sha, Min
3 Shallit, Jeffrey O.
3 Soudry, David
3 Srichan, Teerapat
3 Stănică, Pantelimon
3 Szpruch, Dani
3 Takeda, Shuichiro
3 Technau, Marc
3 Vaughan, Robert C.
3 Wannes, Walid
3 Zhao, Liangyi
2 Ahmadi, Omran
2 Akbary, Amir
2 Alahmadi, Adel N.
2 Altassan, Alaa
2 Baker, Roger C.
2 Bansal, Arpit
2 Bayless, Jonathan
2 Begunts, Aleksandr Vladimirovich
2 Bravo, Eric F.
2 Bravo, Jhon Jairo
2 Brubaker, Ben
2 Brumley, Farrell
2 Bump, Daniel
2 Cai, Yuanqing
2 Chu, Hùng Việt
2 Dai, Lixia
2 Diaconu, Adrian-Viorel
2 Dietmann, Rainer
2 Drmota, Michael
2 Elsholtz, Christian
2 Ford, Kevin B.
2 García, Victor Cuauhtemoc
2 Giri, Sumit
2 Gómez-Colunga, Andrés
2 Granville, Andrew James
2 Güloğlu, Ahmet Muhtar
2 Hanzer, Marcela
2 Harman, Glyn
2 Heyman, Randell
2 Jones, Nathan A.
2 Jørgensen, Palle E. T.
2 Kavaler, Charlotte
2 Klurman, Oleksiy
2 Koukoulopoulos, Dimitris
2 Li, Junxian
2 Liu, Kui
2 Ma, Wu-Xia
2 McDonald, Vaughan
2 McNew, Nathan
2 Mefenza, Thierry
2 Müllner, Clemens
2 Murty, Maruti Ram
2 Oller-Marcén, Antonio M.
2 Pappalardi, Francesco
2 Prabhu, Neha
2 Rajasekaran, Aayush
2 Shoaib, Hatoon
2 Smith, Ethan
2 Spiegelhofer, Lukas
2 Sun, Zhi-Wei
2 Thompson, Lola
2 Vergnaud, Damien
2 Zaharescu, Alexandru
...and 282 more Authors
all top 5

Cited in 98 Serials

44 Journal of Number Theory
22 International Journal of Number Theory
15 Acta Arithmetica
14 Proceedings of the American Mathematical Society
10 Indagationes Mathematicae. New Series
10 The Ramanujan Journal
9 Integers
8 Mathematics of Computation
8 Mathematische Zeitschrift
8 Transactions of the American Mathematical Society
7 Bulletin of the Australian Mathematical Society
7 Monatshefte für Mathematik
6 Periodica Mathematica Hungarica
6 Mathematika
6 Finite Fields and their Applications
6 Journal of the Australian Mathematical Society
6 Chebyshevskiĭ Sbornik
5 Israel Journal of Mathematics
5 Mathematische Annalen
5 Acta Mathematica Hungarica
5 Forum Mathematicum
5 Geometric and Functional Analysis. GAFA
5 Journal de Théorie des Nombres de Bordeaux
4 Archiv der Mathematik
4 Functiones et Approximatio. Commentarii Mathematici
4 Manuscripta Mathematica
4 Experimental Mathematics
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Advances in Mathematics
3 Canadian Mathematical Bulletin
3 Inventiones Mathematicae
3 Taiwanese Journal of Mathematics
3 Journal of Integer Sequences
3 Journal of Mathematical Cryptology
3 Research in the Mathematical Sciences
3 Research in Number Theory
2 Journal of Mathematical Analysis and Applications
2 Mathematical Notes
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Rocky Mountain Journal of Mathematics
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Bulletin of the London Mathematical Society
2 Canadian Journal of Mathematics
2 Compositio Mathematica
2 Duke Mathematical Journal
2 Michigan Mathematical Journal
2 Pacific Journal of Mathematics
2 Quaestiones Mathematicae
2 Revista Matemática Iberoamericana
2 Boletín de la Sociedad Matemática Mexicana. Third Series
2 Journal of the European Mathematical Society (JEMS)
2 Acta Mathematica Sinica. English Series
2 Journal of the Institute of Mathematics of Jussieu
2 Japanese Journal of Mathematics. 3rd Series
2 Science China. Mathematics
1 Analysis Mathematica
1 Discrete Applied Mathematics
1 Information Processing Letters
1 Lithuanian Mathematical Journal
1 Ukrainian Mathematical Journal
1 Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques
1 Annales de l’Institut Fourier
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Colloquium Mathematicum
1 Journal of Algebra
1 Journal of Approximation Theory
1 Journal of Combinatorial Theory. Series A
1 Journal of Functional Analysis
1 Mathematica Slovaca
1 Memoirs of the American Mathematical Society
1 Results in Mathematics
1 Theoretical Computer Science
1 Journal of Complexity
1 Mathematical and Computer Modelling
1 International Journal of Foundations of Computer Science
1 Glasnik Matematički. Serija III
1 Bulletin of the American Mathematical Society. New Series
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 Applicable Algebra in Engineering, Communication and Computing
1 Rad Hrvatske Akademije Znanosti i Umjetnosti. Matematičke Znanosti
1 Turkish Journal of Mathematics
1 Journal of Lie Theory
1 Documenta Mathematica
1 Doklady Mathematics
1 Theory of Computing Systems
1 Journal of Inequalities and Applications
1 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics
1 Annals of Mathematics. Second Series
1 Proceedings of the Steklov Institute of Mathematics
1 Frontiers of Mathematics in China
1 Algebra & Number Theory
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Analysis and Mathematical Physics
1 Afrika Matematika
1 Annales Mathématiques du Québec
1 Discrete Analysis
1 Proceedings of the American Mathematical Society. Series B
1 Transactions of the American Mathematical Society. Series B

Citations by Year