P. Pollack

activity

20152026

most citedAnatomy of torsion in the CM case

3 citations · 6 across the 13 of their papers we have counts for

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Showing 2017Show all

4 papers · 1 filter

math.NT2017

Small prime $k$ th power residues for $k = 2, 3, 4$ : A reciprocity laws approach

Kübra Benli, Paul Pollack

Nagell proved that for each prime $p \equiv 1 (mod 3)$ , $p > 7$ , there is a prime $q < 2 p^{1/2}$ that is a cubic residue modulo $p$ . Here we show that for each fixed $ε > 0$ , and each…

math.NT2017

Typically bounding torsion

Pete L. Clark, Marko Milosevic, Paul Pollack

We formulate the notion of \emph{typical boundedness} of torsion on a family of abelian varieties defined over number fields. This means that the torsion subgroups of elements in t…

math.NT2017

Pursuing polynomial bounds on torsion

Pete L. Clark, Paul Pollack

We show that for all epsilon > 0, there is a constant C(epsilon) > 0 such that for all elliptic curves E defined over a number field F with j(E) in Q we have #E(F)[tors] \leq C(eps…

math.NT2017

Refinements of Lagrange's four-square theorem

Leo Goldmakher, Paul Pollack

A well-known theorem of Lagrange asserts that every nonnegative integer $n$ can be written in the form $a^{2} + b^{2} + c^{2} + d^{2}$ , where $a, b, c, d \in Z$ . We characterize the values…

Small prime kth power residues for k=2,3,4: A reciprocity laws approach

Typically bounding torsion

Pursuing polynomial bounds on torsion

Refinements of Lagrange's four-square theorem

Small prime $k$ th power residues for $k = 2, 3, 4$ : A reciprocity laws approach