Pathikrit Basu
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View article: On Propositions Pertaining to the Riemann Hypothesis IV
On Propositions Pertaining to the Riemann Hypothesis IV Open
In this paper, we enumerate certain hypotheses regarding the Riemann zeta function. The hypotheses are in the form of bounds on the norm of the tail of the sequence that determines the Riemann zeta function and also an optimization problem…
View article: On Sumset Inequalities: A Mathematical Approach
On Sumset Inequalities: A Mathematical Approach Open
In this paper, we study sumset inequalities concerning cardinalities of sumsets and functions of finite subsets of integers such as entropy and additive energy. We also identify sufficient conditions for existence of arithmetic progression…
View article: Prediction and Stochastic Choice
Prediction and Stochastic Choice Open
In this paper, we study a non-parametric approach to prediction in stochastic choice models in economics. We show that VC complexity characterises the predictability of stochastic choice models. We establish prediction methods and provide …
View article: On the Number of Combinations Generating a Sum
On the Number of Combinations Generating a Sum Open
We present some elementary arguments that are applicable to problems in additive combinatorics. In particular, we study the problem of multiple pairs generating the same sum, establishing a general result in the context of an ordered group.
View article: On Propositions Pertaining to the Riemann Hypothesis III
On Propositions Pertaining to the Riemann Hypothesis III Open
In this paper, we consider further propositions concerning the range of possible distributions over the unit circle, for the Riemann zeta function as in prior research. We also derive some new upper bounds on the sum of norms for the tail …
View article: Optimal mechanism design with approximate incentive compatibility and many players
Optimal mechanism design with approximate incentive compatibility and many players Open
We consider a setting in which a mechanism designer must choose the appropriate social alternative depending on the state of nature. We study the problem of optimal design and demonstrate that a mechanism which allocates resources so as to…
View article: On Propositions Pertaining to the Riemann Hypothesis II
On Propositions Pertaining to the Riemann Hypothesis II Open
Aims/Objectives: In this paper, we define certain classes of non-zeroes of the Riemann zeta function. We also present associated algorithms for finding these non-zeroes, which can enable corresponding computations. Some theoretical connect…
View article: On Propositions Pertaining to the Riemann Hypothesis
On Propositions Pertaining to the Riemann Hypothesis Open
In this paper, we establish some methods and propositions that allows a study of the Riemann Hypothesis. The main idea is to divide a sum (finite or infinite), so that the two parts are not equivalent in some sense and hence lead to a non-…
View article: On the Riemann Hypothesis
On the Riemann Hypothesis Open
This paper provides an exact characterisation of the zeroes of the Riemann zeta function. The characterisation is based on a theorem about random vectors, which says that under some conditions, if a vector is always in the convex hull of t…
View article: Perfect i.i.d Processes
Perfect i.i.d Processes Open
This note proves a theorem about i.i.d. i.e. independent and indentically distributed processes, when the index space is a measure space. The statement of the problem corresponding to the theorem proved in this paper appears in [1], in whi…
View article: On the falsifiability and learnability of decision theories
On the falsifiability and learnability of decision theories Open
We study the degree of falsifiability of theories of choice. A theory is easy to falsify if relatively small data sets are enough to guarantee that the theory can be falsified: the Vapnik–Chervonenkis (VC) dimension of a theory is the larg…
View article: Repeated Coordination with Private Learning
Repeated Coordination with Private Learning Open
We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true s…
View article: Learnability and Models of Decision Making under Uncertainty
Learnability and Models of Decision Making under Uncertainty Open
We study whether some of the most important models of decision-making under uncertainty are uniformly learnable, in the sense of PAC (probably approximately correct) learnability. Many studies in economics rely on Savage's model of (subjec…