• MARCH 16 – MARCH 30, 2020
  READING ASSIGNMENT: Until March 30, your reading assignment is the first paper on Laplace Transforms and Sieve Methods. If you have time, read papers 2 and 3.

  I can answer any questions you may have by email. If you need to talk to me about these papers, please send me an email and we can fix a time.

  • A STUDY OF THE MOMENTS OF ADDITIVE FUNCTIONS USING LAPLACE TRANSFORMS AND SIEVE METHODS
  • MOMENTS OF ADDITIVE FUNCTIONSAND THE SEQUENCE OF SHIFTED PRIMES
  • MULTIPLICATIVE FUNCTIONS AND BRUN’S SIEVE
• MARCH 30 – APRIL 10, 2020
  • Selberg’s paper: Note on a Paper by Sathe (1953)
  • Montgomery and Vaughan on Selberg’s paper
  • Appendix on the Gamma Function

  READING ASSIGNMENT: Read Selberg’s paper. This is written in a very compact style. Read also Montgomery-Vaughan’s exposition of Selberg’s paper containing details of calculations. An appendix on the Gamma function is given to you in case you need details on the Hankel contour for the Gamma function.

  I will respond to questions pertaining to this by email during the period Mar 30 to Apr 10.

• APRIL 10 – APRIL 22, 2020
  • de Buijn: On the number of uncancelled elements in the sieve of Eratosthenes (1950)
  • de Bruijn: On integers free of prime factors > y (1951)

  READING ASSIGNMENT:
  Your reading assignment will be the two famous and important papers of de Bruijn. Read first the paper “On the number of uncancelled elements in the sieve of Eratosthenes”. After that, read the paper “On integers free of prime factors > y”. This is is a very important paper on smooth numbers, namely numbers all of whose prime factors are small. I am available by email or phone to answer questions on these papers between April 11 and 22.

Last update April 9, 2020.