Twists of Newforms and Pseudo-Eigenvalues of W-Operators.
Twists of the Iwasawa-Tate Zeta Function.
Two arithmetic functions and asymptotic densities of related sets
Two binary additive problems.
Two Cases of Stark's Conjecture.
Two complete and minimal systems associated with the zeros of the Riemann zeta function
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions. We...
Two congruences involving 4-cores.
Two conjectures by Zhi-Hong Sun
Two conjectures on an addition theorem
Two constructions of the real numbers via alternating series.
Two Diophantine approaches to the irreducibility of certain trinomials
Two Diophantine Systems.
Two divisors of summing up to
In this short note, we give an affirmative answer to a question of Ayad from [1].
Two elementary proofs of Halász's theorem.
Two equations for linear recurrence sequences
Two Exercises Concerning the Degree of the Product of Algebraic Numbers
Two exponential diophantine equations
The equation , to be solved in non-negative rational integers , has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation , to be solved in non-negative rational integers and a rational integer , has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.
Two formulas for successive derivatives and their applications.
Two game-set inequalities.
Two generalized constants related to zero-sum problems for two special sets.