Schedule

• February 19: Organizational meeting
• February 26: Steve Lester (TAU), The Dirichlet divisor problem.
• March 5: Nadav Yesha (TAU), The divisor function in arithmetic progressions and short intervals.
• March 12: Efrat Bank (TAU), Prime polynomials in short intervals
• March 19: Dan Carmon (TAU), The autocorrelation of the Mobius function in F_q[t].
• March 26: Julio Andrade (IHES), The additive divisor problem in F_q[t]
• April 2: Edva Roditty-Gershon (TAU), The variance of sums of the divisor function.
• April 9, 16 - no meeting due to the Passover break
• April 23 Alexei Entin (TAU), The Bateman-Horn conjecture in F_q[t].
• April 30 Maxim Radziwill (IAS Princeton), Sign changes of Fourier coefficients of cusp forms

  Abstract: I'll discuss joint work with Kaisa Matomaki on sign changes of Fourier coefficients of eigencuspforms. I'll motivate the problem and I will explain how and why our work depends on sieve-theoretic analogues of mollifiers. Mollifiers are typically used to understand the zero-distribution of L-functions.

• May 7 Nadav Yesha (TAU) Close divisors

  Abstract: We discuss Tenenbaum's proof of an old conjecture of Erdos about the sum E(n):=∑_i>j1/(d_i - d_j), where d₁ < d₂<... are the divisors of an integer n. Erdos conjectured an upper bound of d(n) for this sum, where d(n) is the number of divisors of n; Tenenbaum was able to prove a strong form of this conjecture, with a bound of E(n)<< d(n)^1-c, with c>5/83.

• May 14: Steve Lester (TAU), The variance of sums of divisor functions in short intervals.

  Given an integer k≥2 the function d_k(n) equals the number of ways of writing n as a product of k positive integers. The variance of sums of the divisor function d₂(n)=d(n) in short intervals was studied by Matti Jutila and later by Aleksandar Ivic. I will discuss work in progress on the variance of sums of d_k(n) in short intervals for k=3. Additionally, I will indicate relationships between this variance and the 2k-th moment of the Riemann zeta-function that I am still trying to understand.

• May 21: Zeev Rudnick (TAU) The distribution of squarefree polynomials.
• May 28: no meeting
• June 4 - no meeting (Shavuot)
• June 11:

Assignments

1. Assignment 1 , due date: March 13, 2014.

2. Assignment 2 , due date: March 26, 2014.

3. Assignment 3 , due date: June 11, 2014.

Contact me at: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 640-7806