• Publications
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Ten lectures on the interface between analytic number theory and harmonic analysis
Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Primes in Short Intervals
Contrary to what would be predicted on the basis of Cramér’s model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x+H)−ψ(x), for 0≤x≤N, is approximately
Minimal theta functions
  • H. Montgomery
  • Mathematics
    Glasgow Mathematical Journal
  • 1 January 1988
Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1. Among such forms, let . The Epstein zeta function of f is denned to be Rankin [7], Cassels [1],
Pair Correlation of Zeros and Primes in Short Intervals
In 1943, A. Selberg [15] Deduced From The Riemann Hypothesis (Rh) that $$\int\limits_{\rm{1}}^{\rm{X}} {{{\left( {\psi \left( {\left( {{\rm{1 + }}\delta } \right){\rm{x}}} \right){\rm{ - }}\psi
A bound for the least prime ideal in the Chebotarev Density Theorem
as x --, oc. In [7] two versions of the Chebotarev density theorem were proved, one unconditional and the other on the assumption of the Generalized Riemann Hypothesis (GRH), each of which expressed
The exceptional set in Goldbach''s problem
An electromagnetic release device for cameras which may selectively be operated continuously comprises a motor circuit, a first switching means adapted to turn the motor circuit on or off, a stopper