19 citations · 88 across the 38 of their papers we have counts for
47 papers
Functional degrees and arithmetic applications III: Beyond Prime Exponent
Pete L. Clark, Uwe Schauz
Continuing our work on group-theoretic generalizations of the prime Ax-Katz Theorem, we give a lower bound on the -adic divisibility of the cardinality of the set of simultaneou…
Functional degrees and arithmetic applications II: The Group-Theoretic Prime Ax-Katz Theorem
Pete L. Clark, Uwe Schauz
We give a version of Ax-Katz's -adic congruences and Moreno-Moreno's -weight refinement that holds over any finite commutative ring of prime characteristic. We deduce this fr…
Densities of integer sets represented by quadratic forms
Pete L. Clark, Paul Pollack, Jeremy Rouse +1
Let be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function , the number of integers of absolute value up to …
CM Elliptic Curves: Volcanoes, Reality and Applications, Part II
Pete L. Clark, Frederick Saia
Let be positive integers, and let be the discriminant of an order in an imaginary quadratic field . When , the first author determined the fiber of the…
CM Elliptic Curves: Volcanoes, Reality and Applications
Pete L. Clark
For positive integers and an order of discriminant in an imaginary quadratic field with discriminant , we determine the fiber of the morphism $X_0(M,N)…
Restricted Variable Chevalley-Warning Theorems
Anurag Bishnoi, Pete L. Clark
We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variabl…