The authors prove: A proper profinite group structure G is projective if and only if G is the absolute Galois group structure of a proper field-valuation structure with block approximation.
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We address the question of recovering the distribution function of a set of orthogonal polynomials from the three term recurrence relation satisfied by the polynomials. We investigate four sets of orthogonal polynomials: the Al-Salam-Chihara polynomials, random walk polynomials …
We address the question of recovering the distribution function of a set of orthogonal polynomials from the three term recurrence relation satisfied by the polynomials. We investigate four sets of orthogonal polynomials: the Al-Salam-Chihara polynomials, random walk polynomials …
This paper is devoted to proving a general partition theorem that asserts the identity of two partition functions, involving the Rogers-Ramanujan and Göllnitz-Gordon identities.
This paper is devoted to the study of equilength two-line arrays of non-negative integers. These are called generalized Frobenius partitions. It is shown that such objects have numerous interactions with modular forms, Kloosterman quadratic forms, the Lusztig-Macdonald-Wall conj…
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form.…
The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a charac…
The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover…
We study the representations of real homogeneous polynomials [italic]p([italic]x) = [italic]p([italic]x₁, ···, [italic]x[italic subscript]n) of even degree [italic]m ([italic]n-ary [italic]m-ics) as sums of [italic]m-th powers of linear forms and generalize the theory of positiv…
The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Dioph…
Introduction Local cohomology groups Global cohomology groups and Selmer structures Kolyvagin systems Kolyvagin systems over principal artinian rings Kolyvagin systems over integral domains Examples Appendix A. Proof of Theorem 3.2.4 Appendix B. Proof of Theorem 4.3.3, by Benjam…
