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Automorphic Forms and L-Functions for the Group Gl(n, R)
- D. Goldfeld, K. Broughan
- Mathematics
- 21 August 2006
Introduction 1. Discrete group actions 2. Invariant differential operators 3. Automorphic forms and L-functions for SL(2,Z) 4. Existence of Maass forms 5. Maass forms and Whittaker functions for…
On the subsequence of primes having prime subscripts
- K. Broughan, A. Barnett
- Mathematics
- 2009
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimates for its counting function. We obtain bounds for the weighted gaps between elements of the…
On the number of solutions of exponential congruences
- A. Balog, K. Broughan, I. Shparlinski
- Mathematics
- 9 March 2010
For a prime $p$ and an integer $a \in \Z$ we obtain nontrivial upper bounds on the number of solutions to the congruence $x^x \equiv a \pmod p$, $1 \le x \le p-1$. We use these estimates to estimate…
The gcd-sum function
- K. Broughan
- Mathematics
- 1 October 2001
The gcd-sum is an arithmetic function defined as the sum of the gcd’s of the first n integers with n : g(n) = P n=1 (i,n). The function arises in deriving asymptotic estimates for a lattice point…
Vanishing of the integral of the Hurwitz zeta Function
- K. Broughan
- MathematicsBulletin of the Australian Mathematical Society
- 1 February 2002
A proof is given that the improper Riemann integral of ζ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with ℜ(s) < 1. The integral does not…
Adic Topologies for the Rational Integers
- K. Broughan
- MathematicsCanadian Journal of Mathematics
- 1 August 2003
Abstract A topology on $\mathbb{Z}$ , which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to $\mathbb{Q}$ , with a…
Fast floating-point processing in Common Lisp
- R. Fateman, K. Broughan, D. Willcock, Duane Rettig
- Computer ScienceTOMS
- 1 March 1995
TLDR
On dominated terms in the general knapsack problem
- Nan Zhu, K. Broughan
- MathematicsOper. Res. Lett.
- 1 August 1997
The Average Order of the Dirichlet Series of the gcd-sum Function
- K. Broughan
- Mathematics
- 2007
Using a result of Bordelles, we derive the second term and improved error expres- sions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.
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