A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A motivic Chebotarev density theorem.
A multidimensional version of a result of Davenport-Erdős.
A multiple set version of the 3k-3 theorem.
A multivariate arithmetic function of combinatorial and topological significance.
A natural extension of Catalan numbers.
A natural prime-generating recurrence.
A natural series for the natural logarithm.
A necessary and sufficient condition for the primality of Fermat numbers
We examine primitive roots modulo the Fermat number . We show that an odd integer is a Fermat prime if and only if the set of primitive roots modulo is equal to the set of quadratic non-residues modulo . This result is extended to primitive roots modulo twice a Fermat number.
A negative answer to two questions about the smallest prime numbers having given digital sums.
A negative result on the representation of modular forms by theta series.
A new algorithm for the computation of logarithmic -class groups of number fields.
A new approach to -Bernoulli numbers and -Bernoulli polynomials related to -Bernstein polynomials.
A new approach to the ElGamal encryption scheme
The ElGamal encryption scheme can be used for both digital signatures and encryption, and its security results from the difficulty of calculating discrete logarithms in a finite field. This algorithm usually works in a multiplicative group of GF(p) and in this case the progress in the discrete logarithm problem forces the users of such a basic ElGamal public key cryptosystem to permanently increase a prime modulus p in order to ensure the desired security. But the task of finding a multiplicative...
A New Characterization of the Integer 5906.
A new class of continued fraction expansions
A new class of infinite products, and Euler's totient.
A new class of -Fibonacci polynomials.
A New Condition for Consecutive Primitive Roots of a Prime.
A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.