If we cn find a nonzero function f suc that f -LRB- s -RRB- zeta -LRB- s -RRB- = f -LRB- 1-s -RRB- zeta -LRB- 1-s -RRB- if and only if Re -LRB- s -RRB- = 1/2 , taking limits as zeta -LRB- s -RRB- tends to zero implies RH ?
If -LSB- math -RSB- f -LRB- 2x -RRB- = -LRB- f -LRB- x -RRB- -RRB- ^ 4 -LSB- / math -RSB- -LSB- math -RSB- \ forall x -LSB- / math -RSB- . Also it is known that -LSB- math -RSB- f -LRB- 0 -RRB- = 1 -LSB- / math -RSB- . Assuming that -LSB- math -RSB- f -LRB- x -RRB- -LSB- / math -RSB- is a continuous function , is it possible to prove that -LSB- math -RSB- \ exp -LRB- kx ^ 2 -RRB- -LSB- / math -RSB- is the only solution ?