33 citations · 44 across the 10 of their papers we have counts for
10 papers
On the sum of in the Piltz divisor problem for and
T. Makoto Minamide, Yoshio Tanigawa, Nigel Watt
Let be the error term in the classical asymptotic formula for the sum , where is the number of ways can be written as a product of…
On eigenfunctions of the kernel
Nigel Watt
The integral kernel () has connections with the Riemann zeta-function and a (recently observed) c…
On eigenvalues of the kernel , II
Nigel Watt
We study the eigenvalues (ordered by modulus) of the integral kernel (). Th…
On eigenvalues of the kernel ()
N. Watt
We show that the kernel () has infinitely many positive eigenvalues and infinitely many negative eigenvalue…
Mertens Sums requiring Fewer Values of the Möbius function
M. N. Huxley, N. Watt
We discuss certain identities involving and , the functions of Möbius and Mertens. These identities allow calculation of , for $d=2,3,4,\ldo…
Mean square of zeta function, circle problem and divisor problem revisited
Jean Bourgain, Nigel Watt
This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically o…
Decoupling for perturbed cones and mean square of
Jean Bourgain, Nigel Watt
An improved estimate is obtained for the mean square of the modulus of the zeta function on the critical line. It is based on the decoupling techniques in harmonic analysis develop…
Weighted fourth moments of Hecke zeta functions with groessencharacters
Nigel Watt
We use recently obtained bounds for sums of Kloosterman sums to bound the sum $\sum_{-D\leq d\leq D} \int_{-D}^D |ζ(1/2+it,λ^d)|^4| \sum_{0<|μ|^2\leq M} A(μ)λ^d((μ)) |μ|^{-2it}|^2…
Weighted spectral large sieve inequalities for Hecke congruence subgroups of SL(2,Z[i])
Nigel Watt
We prove new bounds for weighted mean values of sums involving Fourier coefficients of cusp forms that are automorphic with respect to a Hecke congruence subgroup Γ=Γ_0(q) of the g…
Spectral large sieve inequalities for Hecke congruence subgroups of SL(2,Z[i])
Nigel Watt
We prove, in respect of an arbitrary Hecke congruence subgroup Γ=Γ_0(q_0) of the group SL(2,Z[i]), some new upper bounds (or `spectral large sieve inequalities') for sums involving…