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- Levent Alpoge
- J. Comb. Theory, Ser. A
- 2014

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.

- Salil P. Vadhan, Luca Trevisan, +59 authors Greg Price
- 2012

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)

- Levent Alpoge, Thomas Ang, Luke Schaeffer, Jeffrey Shallit
- DCFS
- 2011

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.

- Levent Alpoge
- Combinatorica
- 2017

- Levent Alpoge
- 2015

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)

- Levent Alpoge, Nadine Amersi, Geoffrey Iyer, Oleg Lazarev, Steven J. Miller, Liyang Zhang
- 2014

1 Levent Alpoge Harvard University, Department of Mathematics, Harvard College, Cambridge, MA 02138 bluealpoge@college.harvard.edu 2 Nadine Amersi Department of Mathematics, University College London, London, WC1E 6BT bluen.amersi@ucl.ac.uk 3 Geoffrey Iyer Department of Mathematics, UCLA, Los Angeles, CA 90095 bluegeoff.iyer@gmail.com 4 Oleg Lazarev… (More)

- Levent Alpoge, Liyang Zhang, Gergely Harcos, Andrew Knightly, Stephen D. Miller, Steve Rallis
- 2013

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)

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