Infinite sets of integers whose distinct elements do not sum to a power.
Small values of the Riemann zeta function on the critical line
We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.
On the error term of the logarithm of the lcm of a quadratic sequence
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [].
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