Some problems of analytic number theory
نویسندگان
چکیده
منابع مشابه
Some Problems in Number Theory
A k = max(p,+ t p,), k < p, < p, + , < 2k . In fact I cannot even disprove f(k) = Ak for all sufficiently large k, though it seems likely that f(k) > Ak for all large k. A well known theorem of Pólya and Störmer states that if u > uo(k) then u(u + 1) always contains a prime factor greater than k, thusf(k) can be determined in a finite number of steps, and an explicit bound has been given by Leh...
متن کاملSome Problems in Additive Number Theory
(3) f(x) = (log x/log 2) + 0(1)? 1\Mloser and I asked : Is it true that f(2 11) >_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) . P. Erdös, Problems and results in additive number theory, Colloque, Théorie des Nombres, Bruxelles 1955, p . 137 . 2. Let 1 < a 1< . . . < ak <_ x be a sequence of integers so that all the sums ai,+ . . .+ais, i 1 <...
متن کاملSome Problems and Results in Number Theory
During my very long life I published many papers of similar title . Here I want to discuss some of my favorite problems many of which go back 50 years and which I hope are still alive and will outlive me . Recently Graham and I published a book entitled "Old and new problems and results in combinatorial number theory" Monographic N ° 28 de L'Enseignement Mathématique, Univ . de Genéve . This bo...
متن کاملSome Applications of Laplace Transforms in Analytic Number Theory
Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...
متن کاملSome Problems in Combinatorial Number Theory
We state and discuss various problems in the general area of arithmetic combinatorics and recent developments related to the ‘sum-product phenomenon’ in the ring of integers, the real and complex numbers and finite fields. In particular, we discuss applications and connections to the theory of exponential sums, Burgess’ estimate, the subspace theorem and to Szemeredi-Trotter type results. In re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1976
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-31-4-313-324