You can add add_filter in wp-config.php, but it is not recommended.
Can you make changes to functions.php? If so, you can try this.
add_filter( 'auto_core_update_send_email', '__return_false' );
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This reply was modified 7 years, 6 months ago by JanrikV.
Have you tried quotes? E.g.
$secret = "RECAPTCHA_KEY";
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This reply was modified 7 years, 6 months ago by JanrikV. Reason: Quotes added