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Starting with a symmetric/antisymmetric matrix with integer coefficients (which we view as an analogue of a metric/form on a principal bundle over the "manifold" Spec Z) we introduce arithmetic analogues of Chern connections and their…
The two squares theorem of Fermat is a gem in number theory, with a spectacular one-sentence "proof from the Book". Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves…
We extend the dipole formalism of Catani and Seymour to QCD processes involving heavy fermions. We give the appropriate subtraction terms together with their integrated counterpart. All calculations are done within dimensional…
An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a…
The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…
We propose three kinds of explicit formulas for the elliptic lambda function by the elliptic modular function. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate some singular values of the…
We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unified perspective to investigate several combinatorial objects…
We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are…
This paper is devoted to the function introduced by M. P. Appell in connection with decomposition of elliptic functions of the third kind into simple elements. We show that this function (which appeared as a Fukaya triple product in…
The renormalized contribution of fermions to the curvature masses of vector and axial-vector mesons is derived with two different methods at leading order in the loop expansion applied to the (2+1)-flavor constituent quark-meson model. The…
In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence…
In Alexandrov's work \cite{al2, al3} it has been shown that the extended partition function $\exp(F^{o,ext}+F^c)$ introduced by Buryak in \cite{bu, bu2} is a tau-function of the KP hierarchy. In this work, we compute the affine coordinates…
After the work of Bordell\`{e}s, Dai, Heyman, Pan and Shparlinki (2018) and Heyman (2019), several authors studied the averages of arithmetic functions over the sequence $[x/n]$ and the integers of the form $[x/n]$. In this paper, we give…
The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are…
We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…
Repeatedly folding a strip of paper in half and unfolding it in straight angles produces a fractal: the dragon curve. Shallit, van der Poorten and others showed that the sequence of right and left turns relates to a continued fraction that…
This talk reviews Feynman integrals, which are associated to elliptic curves. The talk will give an introduction into the mathematics behind them, covering the topics of elliptic curves, elliptic integrals, modular forms and the moduli…
We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
W. L. Ferrar seems to have been the first mathematician to clearly draw a connection between the functional aspects of a summation formula and the behavior of the Dirichlet series underlying it. Taking a formula due to him as a starting…