Schinzel's conjecture H and divisibility in abelian linear recurring sequences
Schinzel's problem: Imprimitive covers and the monodromy method
Schmidt's conjecture on normality for commuting matrices.
Schreiben an Herrn Borchardt über die Theorie der elliptischen Modul-Functionen.
Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Schur's determinants and partition theorems.
Schwache asymptotische Eigenschaften schnellwachsender multiplikativer zahlentheoretischer Funktionen.
Score lists in bipartite multi hypertournaments
Search for Wieferich Primes through the use of Periodic Binary Strings
The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.
Searching for Diophantine quintuples
We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most Diophantine quintuples.
Searching for Kaprekar's constants: algorithms and results.
Searching for large elite primes.
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
Second moments of Dirichlet -functions weighted by Kloosterman sums
For the general modulo and a general multiplicative character modulo , the upper bound estimate of is a very complex and difficult problem. In most cases, the Weil type bound for is valid, but there are some counterexamples. Although the value distribution of is very complicated, it also exhibits many good distribution properties in some number theory problems. The main purpose of this paper is using the estimate for -th Kloosterman sums and analytic method to study the asymptotic properties...
Second moments of holomorphic Hilbert modular forms and subconvexity
Second order modular forms
Second order strong divisibility sequences in an algebraic number field
Sekiguchi-Suwa theory revisited
We present an account of the construction by S. Sekiguchi and N. Suwa of a cyclic isogeny of affine smooth group schemes unifying the Kummer and Artin-Schreier-Witt isogenies. We complete the construction over an arbitrary base ring. We extend the statements of some results in a form adapted to a further investigation of the models of the group schemes of roots of unity.
Selberg Formulae for Gaussian integers
Selberg Zeta function on an exceptional domain.