Location of Repository

We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive and multiplicative) taken on the values of various functions, such as rational and exponential functions; in particular, we obtain upper bounds for such twisted sums

Topics:
Number theory

Year: 2005

OAI identifier:
oai:generic.eprints.org:180/core69

Provided by:
Mathematical Institute Eprints Archive

Downloaded from
http://eprints.maths.ox.ac.uk/180/1/BanksShparJoint.pdf

- (1971). A certain arithmetic sum’,
- (1957). An asymptotic formula in the theory of numbers’,
- (1979). An Introduction to the Theory of Numbers , Fifth Edition, The Clarendon Press,
- (1995). Analogues of Kloosterman sums’,
- (1976). Applications of sieve methods to the theory of numbers ,
- (1974). Basic Number Theory,
- (1999). Character sums with exponential functions and their applications ,
- (1995). Character sums with weights’,
- (2003). Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order’,
- (1995). Fractional parts of functions of a special form’,
- (1985). Incomplete Kloosterman sums and a divisor problem’,
- (2000). New bounds for Gauss sums derived from kth powers, and for Heilbronn’s exponential sum’,
- (1992). On estimates of Gaussian sums and the Waring problem modulo a prime’,
- (1985). On exponential sums involving the divisor function’,
- (1972). On the distribution of digits in periodic fractions’,
- (1957). Primzahlverteilung ,
- (1978). Quasi-Monte Carlo methods and pseudo-random numbers’,
- (1991). The additive divisor problem and exponential sums’, Advances in number theory
- (1978). The asymptotics of a certain arithmetical sum’,
- (1985). The divisor problem for arithmetic progressions’,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.