Related papers: On Ramanujan Master Theorem
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…
An algebraic transformation of the DeTemple-Wang half-integer approximation to the harmonic series produces the general formula and error estimate for the Ramanujan expansion for the nth harmonic number.
Chan and Kumchev studied averages of the first and second moments of Ramanujan sums. In this article, we extend this investigation by estimating the higher moments of averages of Ramanujan sums using the Br\`eteche Tauberian theorem. We…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown.…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ... ], \] where $a_{0} \geq 0$, $a \geq 2$ and $m…
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…
The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and…
In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable…
We make a summary of the different types of proofs adding some new ideas. In addition we conjecture some relations which could be necessary in "modular type proofs" (not still found) of the Ramanujan-like series for 1/\pi^2.
We refine and generalise a Rogers-Ramanujan type partition identity arising from crystal base theory. Our proof uses the variant of the method of weighted words recently introduced by the first author.
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
For unitary groups associated to a ramified quadratic extension of a $p$-adic field, we define various regular formal moduli spaces of $p$-divisible groups with parahoric levels, characterize exceptional special divisors on them, and…
We study the meromorphy of various Euler products of degree two attached to cusp forms including Ramanujan's $\Delta$-function.
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg…
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…