The function Delta(x,N) (which measures the discrepancy of Euler's phi function) as defined in the title is closely associated to several problems in the upper bound sieve.It is also known via a classical theorem of Franel that certain conjectured bounds involving certain averages of Delta(x,N) are equivalent to the Riemann Hypothesis.We improve the unconditional bounds which have been hitherto obtained for Delta(N) and show that these are close to being optimal.
Extremal values of $\Delta(x,N)=\sum\sb {n
CODECA', Paolo;NAIR, Mohan K.
1998
Abstract
The function Delta(x,N) (which measures the discrepancy of Euler's phi function) as defined in the title is closely associated to several problems in the upper bound sieve.It is also known via a classical theorem of Franel that certain conjectured bounds involving certain averages of Delta(x,N) are equivalent to the Riemann Hypothesis.We improve the unconditional bounds which have been hitherto obtained for Delta(N) and show that these are close to being optimal.
CODECA', Paolo;NAIR, Mohan K.
1998
Abstract
The function Delta(x,N) (which measures the discrepancy of Euler's phi function) as defined in the title is closely associated to several problems in the upper bound sieve.It is also known via a classical theorem of Franel that certain conjectured bounds involving certain averages of Delta(x,N) are equivalent to the Riemann Hypothesis.We improve the unconditional bounds which have been hitherto obtained for Delta(N) and show that these are close to being optimal.File in questo prodotto:
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