The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures (1) m(y + 2xy + y âˆ’ x âˆ’ 2x âˆ’ x) = 5 7 m(y + 4xy + y âˆ’ x + x) , which is one of manyâ€¦ (More)

Bjorn Poonen UC Berkeley Abstract: Let P be a convex lattice polygon with one interior lattice point. The number of lattice points on the boundary of P plus the corresponding number for the dualâ€¦ (More)

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-typeâ€¦ (More)

We present a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the character va rieties of representations of theâ€¦ (More)

We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler-Van Wijngaarden. One of the algorithms, for instance, permits oneâ€¦ (More)

This is not immediately obvious (for example, this ratio of factorials is not a product of multinomial coefficients) but it is not hard to prove. The only proof I know proceeds by checking that theâ€¦ (More)

We calculate the E-polynomials of certain twisted GL(n,C)character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-typeâ€¦ (More)

0. In the course of another investigation we came across a sequence of polynomials Pd âˆˆ Z[x, y], such that Pd is absolutely irreducible, of degree d, has low height and at least d + 2d + 3 integralâ€¦ (More)

We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and givesâ€¦ (More)