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pro vyhledávání: '"Clark, Pete"'
Autor:
Clark, Pete L., Schauz, Uwe
Continuing our work on group-theoretic generalizations of the prime Ax-Katz Theorem, we give a lower bound on the $p$-adic divisibility of the cardinality of the set of simultaneous zeros $Z(f_1,f_2,\ldots,f_r)$ of $r$ maps $f_j:A\rightarrow B_j$ bet
Externí odkaz:
http://arxiv.org/abs/2311.10527
Autor:
Clark, Pete L., Schauz, Uwe
We give a version of Ax-Katz's $p$-adic congruences and Moreno-Moreno's $p$-weight refinement that holds over any finite commutative ring of prime characteristic. We deduce this from a purely group-theoretic result that gives a lower bound on the $p$
Externí odkaz:
http://arxiv.org/abs/2305.01304
Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_f(X)$, the number of integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic or $n$ is at least $3$, we s
Externí odkaz:
http://arxiv.org/abs/2304.07399
Autor:
Clark, Pete L., Saia, Frederick
Let $M \mid N$ be positive integers, and let $\Delta$ be the discriminant of an order in an imaginary quadratic field $K$. When $\Delta_K < -4$, the first author determined the fiber of the morphism $X_0(M,N) \rightarrow X(1)$ over the closed point $
Externí odkaz:
http://arxiv.org/abs/2212.13327
Autor:
Clark, Pete L.
For positive integers $M \mid N$ and an order of discriminant $\Delta$ in an imaginary quadratic field $K$ with discriminant $\Delta_K < -4$, we determine the fiber of the morphism $X_0(M,N) \rightarrow X(1)$ over the closed point $J_{\Delta}$ corres
Externí odkaz:
http://arxiv.org/abs/2212.13316
Publikováno v:
In Journal of Algebra 1 December 2024 659:542-580
Autor:
Bishnoi, Anurag, Clark, Pete L.
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 variables restricted to Cartesian products of the Vandermonde subsets of $\F_
Externí odkaz:
http://arxiv.org/abs/2201.11236
Publikováno v:
In Journal of Number Theory March 2024 256:290-328
Autor:
Bourdon, Abbey, Clark, Pete L.
Let $\mathcal{O}$ be an order in the imaginary quadratic field $K$. For positive integers $M \mid N$, we determine the least degree of an $\mathcal{O}$-CM point on the modular curve $X(M,N)_{/K(\zeta_M)}$ and also on the modular curve $X(M,N)_{/\math
Externí odkaz:
http://arxiv.org/abs/1906.07121