On the structure of the Selberg class, IV: basic invariants
On the structure of the Selberg class, VI: non-linear twists
On the structure of (−β)-integers
The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. When β is the analogue of a Parry number, we describe the structure of the set of (−β)-integers by a fixed point of an anti-morphism.
On the subfields of cyclotomic function fields
Let be the rational function field over a finite field of elements. For any polynomial with positive degree, denote by the torsion points of the Carlitz module for the polynomial ring . In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield of the cyclotomic function field of degree over , where is an irreducible polynomial of positive degree and is a positive divisor of . A formula for the analytic class number for the...
On the subgroups of the Picard group.
On the subsequence of primes having prime subscripts.
On the subset sums of exponential type sequences
On the success and failure of Gram's Law and the Rosser Rule
On the sum ... D(n) ... (n + N).
On the sum of a prime and the kth power of a prime
On the sum of consecutive cubes being a perfect square
On the sum of digits of some sequences of integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
On the sum of dilations of a set
We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has .
On the sum of divisors of the Mersenne numbers
On the sum of iterations of the Euler function.
On the sum of the first n values of the Euler function
Let ϕ(n) be the Euler function of n. We put and give an asymptotic formula for the second moment of E(n).
On the sum of the number of divisors in a short segment
On the sum of two integral squares in quadratic fields ℚ(√±p)
On the sum of two squares and two powers of k
It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2.
On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou