Related papers: New conjecture for the $SU_q(N)$ Perk-Schultz mode…
Building on work of M. M\"uger and L. Tuset, we reduce the Mathieu conjecture, formulated by O. Mathieu in 1997, for $SU(N)$ to a simpler conjecture in purely abelian terms. We sketch a similar reduction for $SO(N)$. The proofs rely on…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$-adic approximation in the spirit of Jarn\'ik and…
A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.
We give a general conjecture concerning the existence of Eisenstein congruences between weight $k\geq 3$ newforms of square-free level $NM$ and weight $k$ new Eisenstein series of square-free level $N$. Our conjecture allows the forms to…
We give a new axiomatization of the N-pseudospace, studied in [2] (Tent(2014)) and [1] (Baudisch,Martin-Pizarro,Ziegler(2014)) based on the zigzags introduced in [2]. We also present a more detailed account of the characterization of…
Let Q -> B be a quadric fibration and T -> B a family of sextic du Val del Pezzo surfaces. Making use of the recent theory of noncommutative mixed motives, we establish a precise relation between the Schur-finiteness conjecture for Q, resp.…
In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We prove a continued fraction expansion for the reciprocal of a certain $q$-series. All the specialists in the world are asked whether it is new or not.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
We propose an extension of the Alday-Gaiotto-Tachikawa-Wyllard conjecture to 5d SU(N) gauge theories. A Nekrasov partition function then coincides with the scalar product of the corresponding Gaiotto-Whittaker vectors of the q-deformed W_N…
In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the $Q$-th Farey sequence for $Q\in\mathbb{Z}$ and $Q\geq 2$.
Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.
In this article we prove Crew's parabolicity conjecture of $F$-isocrystals. For this purpose, we introduce and study the notion of $\dagger$-hull of a sub-$F$-isocrystal. On the way, we prove a new Lefschetz theorem for overconvergent…
In terms of Sear's transformation formula for $_4\phi_3$-series, we give new proofs of a summation formula for ${_4\phi_3}$-series due to Andrews [2] and another summation formula for${_4\phi_3}$-series conjectured in the same paper.…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials…