William D. Banks

Papers


1995

The Casselman-Shalika formula for a distinguished model, Proc. Amer. Math. Soc. 123 (1995) no.3, pp.681-692.


1997

Twisted symmetric-square L-functions and the nonexistence of Siegel zeros on GL(3), Duke Math. J., 87 (1997) no.2, pp.343-353.


1998

Heredity of Whittaker models on the metaplectic group, Pacific J. Math., 185 (1998) no.1, pp.89-96.

A corollary to Bernstein's theorem and Whittaker functionals on the metaplectic group, Math. Res. Lett., 5 (1998), pp.781-790.


1999

with J.Levy and M.Sepanski, Block-compatible metaplectic cocycles, J. Reine Angew. Math., 507 (1999), pp.131-163.


2000

with D.Lieman and I.Shparlinski, An identification scheme based on sparse polynomials, Lecture Notes in Comput. Sci., 1751, Springer-Verlag, Berlin (2000).

with F.Griffin, D.Lieman and I.Shparlinski, Nonlinear complexity of the Naor-Reingold pseudo-random function, Lecture Notes in Comput. Sci., 1787, Springer-Verlag, Berlin (2000).

with D.Lieman and I.Shparlinski, An extremely small and efficient identification scheme, Lecture Notes in Comput. Sci., 1841, Springer-Verlag, Berlin (2000).


2001

with D.Lieman, I.Shparlinski, and V.To, Cryptographic applications of sparse polynomials over finite rings, Lecture Notes in Comput. Sci., 2015, Springer-Verlag, Berlin (2001).

with D.Bump and D.Lieman, On the dimension of the Jacquet module of a certain induced representation, Lecture Notes in Pure and Applied Math., 220, Marcel Dekker, Inc., New York (2001).

Some unusual identities for special values of the Riemann zeta function, Ramanujan J., 5 (2001) no.2, pp.153-157.

with I.Shparlinski, Distribution of inverses in polynomials rings, Indag. Math., 12 (2001), pp.303-315.


2002

with I.Shparlinski, On the number of sparse RSA Exponents, J. Number Theory, 95 (2002) no.2, pp.340-350.

with I.Shparlinski, Average normalisations of elliptic curves, Bull. Austral. Math. Soc., 66 (2002), pp.353-358.

with A.Conflitti and I.Shparlinski, Character sums over integers with restricted $g$-ary digits, Illinois J. Math., 46 (2002) no.3, pp.819-836.


2003

with D.Bump and D.Lieman, Whittaker-Fourier coefficients of metaplectic Eisenstein series, Compositio Math., 135 (2003) no.2, pp.153-178.

with A.Harcharras, S.Neuwirth and E.Ricard, Matrix inequalities with applications to the theory of iterated kernels, Linear Algebra Appl., 362 (2003), pp.275-286.

with I.Shparlinski, A variant of NTRU with non-invertible polynomials, Lecture Notes in Comput. Sci., 2551, Springer-Verlag, Berlin (2003).

with A.Harcharras and I.Shparlinski, Short Kloosterman sums for polynomials over finite fields, Canad. J. Math., 55 (2003), pp.225-246.

with A.Harcharras, New examples of noncommutative $Lambda(p)$ sets, Illinois J. Math., 47 (2003), pp.1063-1078.


2004

with A.Conflitti, J.Friedlander and I.Shparlinski, Exponential sums over Mersenne numbers, Compositio Math., 140 (2004), pp.15-30.

with A.Conflitti and I.Shparlinski, Number theoretic designs for directed regular graphs of small diameter, SIAM J. Discrete Math., 17 (2004) no.3, pp.377-383.

with A.van der Poorten, Squares from products of integers, Austral. Math. Soc. Gaz., 31 (2004) no.1, pp.40-42.

with I.Shparlinski, Congruences and exponential sums with the Euler function, in High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS (2004).

with J.Friedlander, C.Pomerance and I.Shparlinski, Multiplicative structure of values of the Euler function, in High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS (2004).

with I.Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arith., 112 (2004) no.4, pp.313-332.

with A.Harcharras, On the norm of an idempotent Schur multiplier on the Schatten class, Proc. Amer. Math. Soc., 132 (2004) no.7, pp.2121-2125.

with A.Harcharras and I.Shparlinski, Smooth values of shifted primes in arithmetic progressions, Michigan Math. J., 52 (2004) no.3, pp.603-618.

with D.Hart and M.Sakata, Almost all palindromes are composite, Math. Res. Lett., 11 (2004) nos.5-6, pp.853-868.


2005

with R.Heath-Brown and I.Shparlinski, On the average value of divisor sums in arithmetic progressions, Internat. Math. Res. Notices, 2005, no.1, pp.1-26.

with F.Luca, Concatenations with binary recurrent sequences, J. Integer Seq., 8 (2005), no.1, Article 05.1.3, 18pp.(Electronic)

with F.Luca, I.Shparlinski and H.Stichtenoth, On the value set of $n!$ modulo a prime, Turkish J. Math., 29 (2005), 169-174.

with F.Luca and I.Shparlinski, Irrationality of power series for various number theoretic functions, Manuscripta Math., 117 (2005), no.2, 183-197.

with F.Luca, F.Saidak and I.Shparlinski, Values of arithmetical functions equal to a sum of two squares, Quart. J. Math. Oxford Ser., 56 (2005), 123-139.

with F.Luca, Nonaliquots and Robbins numbers, Colloq. Math., 103 (2005), 27-32.

with K.Ford, F.Luca, F.Pappalardi and I.Shparlinski, Values of the Euler function in various sequences, Monatsh. Math., 146 (2005), 1-19.

with F.Luca, F.Saidak and P.Stu anicu a, Compositions with the Euler and Carmichael functions, Abh. Math. Sem. Hamburg, 75 (2005), 215-243.

with M.Garaev, F.Luca and I.Shparlinski, Uniform distribution of the fractional part of the average prime divisor, Forum Math., 17 (2005), 885-901.

Towards faster cryptosystems, II, in Public Key Cryptography, Proceedings of Symposia in Pure Mathematics, 62, AMS, 2005.

with F.Luca, Roughly squarefree values of the Euler and Carmichael functions, Acta Arith. 120 (2005), 211-230.

with I.Shparlinski, Prime divisors of palindromes, Period. Math. Hungar. 51 (2005), 1-10.

with F.Luca and I.Shparlinski, Some divisibility properties of the Euler function, Glasgow Math. J. 47 (2005), no.3, 517-528.

with G.Harman and I.Shparlinski, Distributional properties of the largest prime factor, Michigan Math. J. 53 (2005), 665-681.


2006

with F.Luca and I.Shparlinski, Arithmetic properties of $\varphi(n)/\lambda(n)$ and the structure of the multiplicative group modulo $n$, Comment. Math. Helv. 81 (2006), no.1, 1-22.

with J.Friedlander, S.Konyagin and I.Shparlinski, Incomplete character sums and Diffie-Hellman triples, Math. Proc. Cambridge Philos. Soc. 140 (2006), 193-206.

with J.Friedlander, F.Luca, F.Pappalardi and I.Shparlinski, Coincidences in the values of the Euler and Carmichael functions, Acta Arith. 122 (2006) no.3, 207-234.

with I.Shparlinski, Non-residues and primitive roots in Beatty sequences, Bull. Austral. Math. Soc. 73 (2006), 433-443.

with F.Luca, On integers with a special divisibility property, Arch. Math. (Brno) 42 (2006), 31-42.

with I.Shparlinski, Multiplicative character sums with the $g$-ary sum of digits function, Ramanujan J. 11 (2006) no.2, 215-219.

with J.Friedlander, M.Garaev and I.Shparlinski, Double character sums over elliptic curves and finite fields, Pure Appl. Math. Q. 2 (2006) no.1, 179-197.

with I.Shparlinski, Short character sums with Beatty sequences, Math. Res. Lett. 13 (2006), 539-547.

with J.Friedlander, M.Garaev and I.Shparlinski, Character sums with exponential functions over smooth numbers, Indag. Math. (N.S.) 17 (2006), no.2, 157-168.

with F.Pappalardi, Values of the Euler function free of $k$-th powers, J. Number Theory 120 (2006) no.2, 326-348.

with I.Shparlinski, Congruences and rational exponential sums with the Euler function, Rocky Mountain J. 36 (2006), 1415-1426.

with F.Luca and I.Shparlinski, Common divisors of the Euler function at related arguments, Acta Sci. Math. (Szeged) 72 (2006), no.3-4, 525-536.

with I.Shparlinski, Average value of the Euler function on binary palindromes, Bull. Pol. Acad. Sci. Math. 54 (2006), no.2, 95-101.

with I.Shparlinski, Prime divisors of Beatty sequences, J. Number Theory 123 (2007) no.2, 413-425.

with F.Luca and I.Shparlinski, On rough and smooth neighbours, Rev. Mat. Complut. 20 (2007) no.1, 109-118.

with I.Shparlinski, On values taken by the largest prime factor of shifted primes, J. Aust. Math. Soc. 82 (2007), 133-147.


2007

with I.Shparlinski, Integers with a large smooth divisor, Integers 7 (2007), A17, 11pp. (electronic)

with F.Luca, Sums of prime divisors and Mersenne numbers, Houston J. Math. 33 (2007), no.2, 403-413 (electronic).

with F.Luca, When the sum of aliquots divides the totient, Proc. Edinb. Math. Soc. 50 (2007), 563-569.

with F.Luca, Composite integers $n$ for which $\varphi(n)\mid n-1$, Acta Math. Sinica, English Series 23 (2007), no.10, 1915-1918.

with M.Sakata and F.Saidak, Kloosterman sums for modified van der Corput sequences, Uniform Distribution Theory 2 (2007), no.1, 39-52.