Results 11 to 20 of about 1,373 (81)

THE MOONSHINE MODULE FOR CONWAY’S GROUP

Forum of Mathematics, Sigma, 2015
We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing ...
JOHN F. R. DUNCAN, SANDER MACK-CRANE
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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE

Forum of Mathematics, Pi, 2015
Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
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On the algebraicity of coefficients of half-integral weight mock modular forms

Open Mathematics, 2018
Extending works of Ono and Boylan to the half-integral weight case, we relate the algebraicity of Fourier coefficients of half-integral weight mock modular forms to the vanishing of Fourier coefficients of their shadows.
Choi SoYoung, Kim Chang Heon
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Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80 [PDF]

, 2009
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their ...
Elkies, Noam D., Kominers, Scott D.
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On the Mahler measure of hyperelliptic families

, 2017
We prove Boyd’s “unexpected coincidence” of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials y³ − y + x³ − x + kxy whose zero loci define
Bertin, M., Zudilin, W.
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Lost in translation

, 2012
We explain the use and set grounds about applicability of algebraic transformations of arithmetic hypergeometric series for proving Ramanujan's formulae for $1/\pi$ and their generalisations.Comment: 6 ...
Zudilin, Wadim
core   +1 more source

A generating function of the squares of Legendre polynomials

, 2012
We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
core   +1 more source

Enhancement of Kondo effect in quantum dots with an even number of electrons

, 2000
We investigate the Kondo effect in a quantum dot with almost degenerate spin-singlet and triplet states for an even number of electrons. We show that the Kondo temperature as a function of the energy difference between the states Delta reaches its ...
A. C. Hewson, A. Kawabata, D. Goldhaber-Gordon, D. Goldhaber-Gordon, D. L. Cox, F. D. M. Haldane, F. Simmel, I. Okada, J. Kondo, K. Yosida, L. I. Glazman, L. I. Glazman, L. P. Kouwenhoven, M. Pustilnik, Mikio Eto, P. Nozières, P. W. Anderson, S. Hershfield, S. M. Cronenwett, S. Sasaki, S. Tarucha, T. Inoshita, T. K. Ng, T. Pohjola, W. Izumida, Y. Meir, Yuli V. Nazarov   +26 more
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
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The tenth order mock theta functions revisited

, 2009
In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan's lost notebook. These were originally proved by Choi.
Zwegers, Sander
core   +1 more source