Establishes sharp lower bounds matching prior upper bounds for moments of short character sums, zeta sums, and twisted sums with multiplicative weights, for x up to r^0.499.
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Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights
Establishes sharp lower bounds matching prior upper bounds for moments of short character sums, zeta sums, and twisted sums with multiplicative weights, for x up to r^0.499.