Related papers: Interpolated sequences and critical $L$-values of …

Let L >= 3. Using the moduli interpretation, we define certain elliptic modular forms of level Gamma(L) over any field k where 6L is invertible and k contains the Lth roots of unity. These forms generate a graded algebra R_L, which, over C,…

In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to…

Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $\infty$), which interpolates the complex…

Let f be a modular form of weight 2 and trivial character. Fix also an imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic Zp-extension of…

We study the critical properties of the monopole-percolation transition in U(1) lattice gauge theory coupled to scalars at infinite ($\beta=0$) gauge coupling. We find strong scaling corrections in the critical exponents that must be…

We consider the case of several scalar fields, charged under a number of U(1) factors, acquiring vacuum expectation values due to an anomalous U(1). We demonstrate how to make redefinitions at the superfield level in order to account for…

We extend a result of Greenberg and Stevens on the interpolation of modular symbols in Hida families to the context of non-split rational quaternion algebras. Both the definite case and the indefinite case are considered.

Available proofs of result of the type 'at least one of the odd zeta values $\zeta(5),\zeta(7),\dots,\zeta(s)$ is irrational' make use of the saddle-point method or of linear independence criteria, or both. These two remarkable techniques…

We consider polynomials that are orthogonal over an analytic Jordan curve L with respect to a positive analytic weight, and show that each such polynomial of sufficiently large degree can be expanded in a series of certain integral…

Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${}_2F_1(1)$ hypergeometric series and Ramanujan's theory of…

In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on the study of the two-variable analogues of these conjectures…

Let $p$ be an odd prime integer, $F/\mathbb{Q}$ be an imaginary quadratic field, and $\Psi$ be a small slope cuspidal Bianchi modular form over $F$ which is non-ordinary at $p$. In this article, we first construct a $p$-adic distribution…

We prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall's identity for the generalized hypergeometric function…

In the 1980s B\"ocherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin L-function attached to a Siegel modular form $F$ to the Fourier coefficients of $F$. This conjecture has been proved…

We develop two structure theorems for vector valued Siegel modular forms for Igusa's subgroup \Gamma_2[2,4], the multiplier system induced by the theta constants and the representation Sym^2. In the proof, we identify some of these modular…

Let $p$ be an odd prime, $N$ a square-free odd positive integer prime to $p$, $\pi$ a $p$-ordinary cohomological irreducible cuspidal automorphic representation of $\mathrm{GSp}_4(\mathbb{A}_\mathbb{Q})$ of principal level $N$ and Iwahori…

We provide a modular construction of the Laza--Sacc\`a--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-K\"ahler…

We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for \Gamma_0(2). Numerical evidence indicates that a sharper bound holds for the…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…