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We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when…

We prove a result on the distribution of the general divisor functions in arithmetic progressions to smooth moduli which exceed the square root of the length.

We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give…

False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular…

The modular invariant of rank 1 Drinfeld modules is introduced and used to formulate and prove an exact analog of the Weber-Fueter theorem for global function fields. The main ingredient in the proof is a version of Shimura's Main Theorem…

We apply inequalities from the theory of linear forms in logarithms to deduce effective results on S-integral points on certain higher-dimensional varieties when the cardinality of S is sufficiently small. These results may be viewed as a…

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We give a method of representing the modular invariant function by generators of a modular function field.

We discuss the structure of finite groups for which the projective indecomposable modules have special given dimensions. In particular, we prove the converse of Fong's dimension formula for $p$-solvable groups. Furthermore, we characterize…

In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.

We examine the large volume compactification of Type IIB string theory or its F theory limit and the associated supersymmetry breakdown and soft terms. It is crucial to incorporate the loop-induced moduli mixing, originating from radiative…

Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…

We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…

We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…

We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.