Number theory

36 problems

Can rational torsion be bounded by abelian-variety dimension and number-field degree?

Do all Galois-invariant cohomology classes of the relevant degree come from algebraic cycles over a finite field?

Can finite arithmetic orbits be bounded by map degree and number-field degree alone?

Can an Euler totient value come from exactly one positive integer?

Are the local components of every cuspidal automorphic representation of GLn tempered?

Must an additive basis of nonnegative integers have arbitrarily many representations of some sums?

Does the arithmetic fundamental group of a curve identify exactly its rational points?

How far can averaged control of prime-counting errors in arithmetic progressions extend as the modulus grows?

Do non-CM elliptic curves over the rationals always have full mod-p Galois image for primes p>37?

Is every coefficient of Ramanujan’s discriminant modular form nonzero?

Do all finite strings of decimal digits occur in π with the frequencies expected from uniformly chosen digits?

For each fixed positive gap, are there only finitely many distinct pairs of integer perfect powers separated by that gap?