Related papers: On Ramanujan Master Theorem
Ramanujan's approximation to the exponential function is reexamined with the help of Perron's saddle-point method. This allows for a wide generalization that includes the results of Buckholtz, and where all the asymptotic expansion…
We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.
This is a lecture on the theory of formal power series developed entirely without any analytic machinery. Combining ideas from various authors we are able to prove Newton's binomial theorem, Jacobi's triple product, the Rogers--Ramanujan…
The present note generalizes Debarre's Bertini-type results for in- verse images of Schubert varieties with the extension of formal func- tions.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic…
This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
The near orthgonality of certain $k$-vectors involving the Ramanujan sums were studied by E. Alkan in [J. Number Theory, 140:147--168 (2014)]. Here we undertake the study of similar vectors involving a generalization of the Ramanujan sums…
In this article we establish some formalism of Derived Witt-D\'evissage theory for resolving subcategories of abelian categories. Results directly apply to noetherian schemes.
We develop a theory of separable ring extensions and separable functors for nonunital rings in the setting of firm modules. We prove nonunital analogues of classical results on functorial separability and semisimplicity, and apply these…
There are several astrophysical configurations where one is interested only in the long-term dynamical evolution. Although the first-order version of this approximation is usually sufficient in applications, second-order corrections may be…
In this paper, the formal derivative operator defined with respect to context-free grammars is used to prove some properties about binomial coefficients and multifactorial numbers. In addition, we extend the formal derivative operator to…
We consider an extension of the Ramanujan series with a variable $x$. If we let $x=x_0$, we call the resulting series: "Ramanujan series with the shift $x_0$". Then, we relate these shifted series to some $q$-series and solve the case of…
The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating…
We show that the absolute convergence of a Ramanujan expansion does not guarantee the convergence of its real variable generalization, which is obtained by replacing the integer argument in the Ramanujan sums with a real number. We also…
We make some simple observations on basic issues pertaining to thermostatistical formalisms.