On automorphisms of quaternion orders.
On -sequences
Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a -sequence A satisfies . The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof of Erdős’...
On B. Segre's construction of an ovaloid
On Bachet's Diophantine Equation x... = y... + k.
On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms
We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.
On Baker type lower bounds for linear forms
A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers over the ring of an imaginary quadratic field . This work deals with the simultaneous auxiliary functions case.
On Balancing and Lucas-balancing Quaternions
The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
On Bases for ...-Finite Groups.
On bases with a -order.
On basis problem for Siegel modular forms of degree 2
On Bernoulli and Euler Numbers.
On Bernoulli identities and applications.
Bernoulli numbers appear as special values of zeta functions at integers and identities relating the Bernoulli numbers follow as a consequence of properties of the corresponding zeta functions. The most famous example is that of the special values of the Riemann zeta function and the Bernoulli identities due to Euler. In this paper we introduce a general principle for producing Bernoulli identities and apply it to zeta functions considered by Shintani, Zagier and Eie. Our results include some of...
On Best Two-Dimensional Dirichlet-Approximations and their Algorithmic Calculation.
On Bialostocki's conjecture for zero-sum sequences
On Bilinear Structures on Divisor Class Groups
It is well known that duality theorems are of utmost importance for the arithmetic of local and global fields and that Brauer groups appear in this context unavoidably. The key word here is class field theory.In this paper we want to make evident that these topics play an important role in public key cryptopgraphy, too. Here the key words are Discrete Logarithm systems with bilinear structures.Almost all public key crypto systems used today based on discrete logarithms use the ideal class groups...
On Binary Equations.
On binary quartic forms.
On binary representations of integers with digits .
On binomial sums for the general second order linear recurrence.
On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I