69,535 research outputs found
Fermion Systems in Discrete Space-Time - Outer Symmetries and Spontaneous Symmetry Breaking
A systematic procedure is developed for constructing fermion systems in
discrete space-time which have a given outer symmetry. The construction is
illustrated by simple examples. For the symmetric group, we derive constraints
for the number of particles. In the physically interesting case of many
particles and even more space-time points, this result shows that the
permutation symmetry of discrete space-time is always spontaneously broken by
the fermionic projector.Comment: 43 pages, LaTeX, few typos corrected (published version
Simple zeros of modular L-functions
Assuming the generalized Riemann hypothesis, we prove quantitative estimates
for the number of simple zeros on the critical line for the L-functions
attached to classical holomorphic newforms.Comment: 46 page
Extreme values of the Riemann zeta function and its argument
We combine our version of the resonance method with certain convolution
formulas for and . This leads to a new
result for : The maximum of on the interval
is at least . We also obtain conditional results for
times the argument of and . On
the Riemann hypothesis, the maximum of is at least and the maximum of is at least on the interval whenever .Comment: This is the final version of the paper which has been accepted for
publication in Mathematische Annale
Finding all equilibria in games of strategic complements
I present a simple and fast algorithm that finds all the pure-strategy Nash equilibria in games with strategic complementarities. This is the first non-trivial algorithm for finding all pure-strategy Nash equilibria
Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary
code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1)
where V(n,d) stands for the volume of a Hamming ball of radius d. Recently
Jiang and Vardy showed that for binary non-linear codes this bound can be
improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In
this paper we show that certain asymptotic families of linear binary [n,n/2]
random double circulant codes satisfy the same improved Gilbert-Varshamov
bound.Comment: Submitted to IEEE Transactions on Information Theor
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