My solution, updated in response to Jamal and vnp:

#include <fstream>
#include <iostream>
using namespace std;

const size_t DIGITS_IN_PRODUCT = 13;

void refill_window(string &series, size_t &i, uint8_t* window);
uint64_t window_product(uint8_t* window);

int main() {
  // read series.txt into a string without newline characters
  ifstream ifs("../series.txt");
  string series, line;
  while (getline(ifs, line)) {
    series += line;
  }
  ifs.close();
  if (series.size() < DIGITS_IN_PRODUCT) {
    cout << "Error: series.txt contains too few elements." << endl;
    exit(2);
  }
  uint8_t window[DIGITS_IN_PRODUCT];
  for (size_t i = 0; (i < DIGITS_IN_PRODUCT) && (i < series.length());
       i++) {
    if (series[i] == '0') {
      refill_window(series, i, window);
      break;
    }
    window[i] = series[i] - '0';
  }
  uint64_t product = window_product(window);
  uint64_t max_product = product;
  for (size_t i = DIGITS_IN_PRODUCT; i < series.length(); i++) {
    if (series[i] == '0') {
      refill_window(series, i, window);
      product = window_product(window);
    } else {
      product /= window[i % DIGITS_IN_PRODUCT];
      window[i % DIGITS_IN_PRODUCT] = series[i] - '0';
      product *= window[i % DIGITS_IN_PRODUCT];
    }
    if (product > max_product) {
      max_product = product;
    }
  }
  cout << max_product << endl;
}

void refill_window(string &series, size_t &i, uint8_t* window) {
  i++;
  for (size_t j = 0;
       (j < DIGITS_IN_PRODUCT) && (i < series.length()); j++, i++) {
    if (series[i] == '0') {
      refill_window(series, i, window);
      return;
    }
    window[i % DIGITS_IN_PRODUCT] = series[i] - '0';
  }
  i--; // correct for final increment in for loop.
}

uint64_t window_product(uint8_t* window) {
  uint64_t product = 1;
  for (size_t i = 0; i < DIGITS_IN_PRODUCT; i++) {
    product *= window[i];
  }
  return product;
}