arXiv subjects
Publications and source records attributed to P. D. T. A. Elliott.
The authors review results implicit in their recent paper [2] on the product/quotient representation of rationals by rationals of the type $( an + b )/ ( An+ B )$ and give a detailed account of a particular related non-intuitive simultaneous ( i.e. two dimensional ) representation of pairs of rationals.
Classical mean-value results of Wirsing type in analytic number theory are established under weaker than classical conditions.
The authors show how to determine the group generated by the ratios $(an+b)/(An+B)$ through its dual.
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression and to the Fourier coefficients of automorphic cusp forms.
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression and to the Fourier coefficients of automorphic cusp forms.
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
An inequality of Large Sieve type, efficacious in the analytic treatment of Euler products, is obtained.
An effective search bound is established for the least non-trivial integer zero of an arbitrary integral cubic form in at least 17 variables.
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.