Number Theory » Additive N.T.

Are there an infinite number of lucky primes? ★

Author(s): Lazarus: Gardiner: Metropolis; Ulam

Conjecture   If every second positive integer except 2 is remaining, then every third remaining integer except 3, then every fourth remaining integer etc. , an infinite number of the remaining integers are prime.

Keywords: lucky; prime; seive

Posted by cubola zaruka
updated March 24th, 2010
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Analysis

Something like Picard for 1-forms ★★

Author(s): Elsner

Conjecture   Let $ D $ be the open unit disk in the complex plane and let $ U_1,\dots,U_n $ be open sets such that $ \bigcup_{j=1}^nU_j=D\setminus\{0\} $. Suppose there are injective holomorphic functions $ f_j : U_j \to \mathbb{C}, $ $ j=1,\ldots,n, $ such that for the differentials we have $ {\rm d}f_j={\rm d}f_k $ on any intersection $ U_j\cap U_k $. Then those differentials glue together to a meromorphic 1-form on $ D $.

Keywords: Essential singularity; Holomorphic functions; Picard's theorem; Residue of 1-form; Riemann surfaces

Posted by MathOMan
updated February 26th, 2010
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Graph Theory

Odd cycles and low oddness ★★

Author(s):

Conjecture   If in a bridgeless cubic graph $ G $ the cycles of any $ 2 $-factor are odd, then $ \omega(G)\leq 2 $, where $ \omega(G) $ denotes the oddness of the graph $ G $, that is, the minimum number of odd cycles in a $ 2 $-factor of $ G $.

Keywords:

Posted by Gagik
updated December 13th, 2011
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