- Full text PDF available (8)
- This year (1)
- Last 5 years (7)
- Last 10 years (8)
Journals and Conferences
We prove that the number of partitions of an integer into at most b distinct parts of size at most n forms a unimodal sequence for n sufficiently large with respect to b. This resolves a recent conjecture of Stanley and Zanello.
This is a survey of pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number… (More)
The Katz-Sarnak density conjecture states that the scaling limits of the distributions of zeroes of families of automorphic L-functions agree with the scaling limits of eigenvalue distributions of classical subgroups of the unitary groups U(N). This conjecture is often tested by way of computing particular statistics, such as the one-level density, which… (More)
Given a formal language L specified in various ways, we consider the problem of determining if L is nonempty. If L is indeed nonempty, we find upper and lower bounds on the length of the shortest string in L.
We prove that, when elliptic curves E/Q are ordered by height, the average number of integral points #|E(Z)| is bounded, and in fact is less than 66 (and at most 8 9 on the minimalist conjecture). By “E(Z)” we mean the integral points on the corresponding quasiminimal Weierstrass model EA,B : y2 = x3 + Ax + B with which one computes the naı̈ve height. The… (More)
1 Levent Alpoge Harvard University, Department of Mathematics, Harvard College, Cambridge, MA 02138 email@example.com 2 Nadine Amersi Department of Mathematics, University College London, London, WC1E 6BT firstname.lastname@example.org 3 Geoffrey Iyer Department of Mathematics, UCLA, Los Angeles, CA 90095 email@example.com 4 Oleg Lazarev… (More)
The Katz-Sarnak Density Conjecture states that the behavior of zeros of a family of L-functions near the central point (as the conductors tend to zero) agrees with the behavior of eigenvalues near 1 of a classical compact group (as the matrix size tends to infinity). Using the Petersson formula, Iwaniec, Luo and Sarnak [ILS] proved that the behavior of… (More)