823 citations
- Max Planck Institute for Extraterrestrial PhysicsDE32 papers
- Center for Astrophysics Harvard & SmithsonianUS27 papers
- University of Maryland, College ParkUS25 papers
- Centre National de la Recherche ScientifiqueFR22 papers
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- National Institute for AstrophysicsIT19 papers
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7 papers · 1 filter
Finding normal bases over finite fields with prescribed trace self-orthogonal relations
Xiyong Zhang, Rongquan Feng, Qunying Liao +1
Normal bases and self-dual normal bases over finite fields have been found to be very useful in many fast arithmetic computations. It is well-known that there exists a self-dual no…
Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
Kevin James, Ethan Smith
Let be a fixed number field, assumed to be Galois over . Let and be fixed integers with positive. Given an elliptic curve , defined over , we consi…
A generalization of the Barban-Davenport-Halberstam Theorem to number fields
Ethan Smith
For a fixed number field , we consider the mean square error in estimating the number of primes with norm congruent to modulo by the Chebotarëv Density Theorem when aver…
Finite field elements of high order arising from modular curves
Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao +6
In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit…
Elliptic curves, modular forms, and sums of Hurwitz class numbers
Brittany Brown, Neil J. Calkin, Timothy B. Flowers +3
Let H(N) denote the Hurwitz class number. It is known that if is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the beha…
Pullbacks of Siegel Eisenstein Series and Weighted Averages of Critical -values
Nadine Amersi, Jeffrey Beyerl, Jim Brown +2
In this paper we obtain a weighted average formula for special values of -functions attached to normalized elliptic modular forms of weight and full level. These results are…