{'fraction_non_alphanumeric': 0.017578125, 'fraction_numerical': 0.0, 'mean_word_length': 5.107142857142857, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
NONPOSITIVITY OF CERTAIN FUNCTIONS ASSOCIATED WITH ANALYSIS ON ELLIPTIC SURFACE

In this paper, we study some basic analytic properties of the boundary term of Fesenko’s two-dimensional zeta integrals. In the case of the rational number field, this term is the Laplace transform of certain infinite series consisting of KBessel functions. The positivity property of the fourth log derivative of such series is closely related to the Riemann hypothesis for the Hasse-Weil L-function attached to an elliptic curve.