# Anomalous primes and the elliptic Korselt criterion

@article{Babinkostova2016AnomalousPA, title={Anomalous primes and the elliptic Korselt criterion}, author={Liljana Babinkostova and Jackson C. Bahr and Yujin H. Kim and Eric Neyman and Gregory K. Taylor}, journal={Journal of Number Theory}, year={2016} }

## 4 Citations

### On Types of Elliptic Pseudoprimes

- Mathematicsjournal of Groups, Complexity, Cryptology
- 2021

We generalize the notions of elliptic pseudoprimes and elliptic Carmichael
numbers introduced by Silverman to analogues of Euler-Jacobi and strong
pseudoprimes. We investigate the relationships among…

### G R ] 1 5 O ct 2 01 7 ON TYPES OF ELLIPTIC PSEUDOPRIMES

- Mathematics
- 2017

Abstract. We generalize Silverman’s [19] notions of elliptic pseudoprimes and elliptic Carmichael numbers to analogues of Euler-Jacobi and strong pseudoprimes. We inspect the relationships among…

### The $p$-adic limits of class numbers in $\mathbb{Z}_p$-towers

- Mathematics
- 2022

. This article discusses variants of Weber’s class number problem in the spirit of arithmetic topology. Let p be a prime number. We ﬁrst prove the p -adic convergence of class numbers in a Z p…

### Statistics for Iwasawa invariants of elliptic curves

- MathematicsTransactions of the American Mathematical Society
- 2021

We study the average behaviour of the Iwasawa invariants for the Selmer groups of elliptic curves, setting out new directions in arithmetic statistics and Iwasawa theory.

## References

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### On Types of Elliptic Pseudoprimes

- Mathematicsjournal of Groups, Complexity, Cryptology
- 2021

We generalize the notions of elliptic pseudoprimes and elliptic Carmichael
numbers introduced by Silverman to analogues of Euler-Jacobi and strong
pseudoprimes. We investigate the relationships among…

### INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS

- MathematicsJournal of the Australian Mathematical Society
- 2012

Abstract In 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat’s little theorem, but based instead on the arithmetic of elliptic curves with complex…

### On the number of elliptic pseudoprimes

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For an elliptic curve E with complex multiplication by an order in K = Q(V\/d), a point P of infinite order on E, and any prime p with (-d I p) = -1, we have that (p + 1) * P = O(mod p), where 0 is…

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In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational…

### Elliptic Carmichael Numbers and Elliptic Korselt Criteria

- Mathematics
- 2011

Let E/Q be an elliptic curve, let L(E,s)=\sum a_n/n^s be the L-series of E/Q, and let P be a point in E(Q). An integer n > 2 having at least two distinct prime factors will be be called an elliptic…

### PRIMALITY OF THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD

- Mathematics
- 1988

Given a fixed elliptic curve E defined over Q having no rational torsion points, we discuss the probability that the number of points on E mod/? is prime as the prime p varies. We give conjectural…

### A classical introduction to modern number theory

- MathematicsGraduate texts in mathematics
- 1982

This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.

### Anomalous primes of the elliptic curve ED: y2*x3+D

- Mathematics
- 2016

Let D∈Z be an integer that is neither a square nor a cube in Q(−3), and let ED be the elliptic curve defined by y2=x3+D. Mazur conjectured that the number of anomalous primes less than N should be…

### The distribution of Lucas and elliptic pseudoprimes

- Mathematics
- 1991

Let L(x) denote the counting function for Lucas pseudoprimes, and E(x) denote the elliptic pseudoprime counting function. We prove that, for large x, L(x) ≤ x L(x) 1/2 and E(x) ≤ x L(x) 1/3 , where…