Large language models (LLMs) are increasingly used in academic research workflows, but scholarly tasks require high factual precision and therefore expose a key weakness: overconfidence. Here, overconfidence is defined behaviorally as the tendency to produce confident, assertive, and well-formatted outputs even when the underlying knowledge is incomplete or unverifiable, rather than as a calibration gap between stated confidence and accuracy. To examine this issue, we introduce GIScholarBench, a benchmark built from 10,865 papers published in 25 core GIScience journals between 2020 and 2025. The benchmark covers three tasks with increasing cognitive complexity: metadata retrieval, literature linking, and research direction generation. We evaluate Claude Sonnet 4.5, Gemini 3, and ChatGPT 5.3 through their native web interfaces under real-world user-facing conditions. Results show consistent overconfidence across all tasks. In metadata retrieval, ChatGPT 5.3 achieves the highest accuracy, but all models still generate definitive titles and DOIs when predictions are wrong. In literature linking, Claude Sonnet 4.5 recovers the most references, but all models show a clear gap between top-ranked retrieval and longer citation lists, suggesting that references are extended beyond reliable retrieval capacity. In research direction generation, AI-generated directions show lower topic coverage, higher novel miss rates, and lower semantic diversity than real future-citing papers. These findings suggest that LLM overconfidence is task-invariant but takes different forms: factual overgeneration in retrieval, unreliable citation expansion in literature linking, and overconfidence in output completeness during research ideation.